Papers

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Below are some papers related to my current research:

Ahlgren, Scott; Boylan, Matthew; Coefficients of half-integral weight modular forms modulo $\ell^j$. Math. Ann. 331 (2005), no. 1, 219–239. (doi, MR, notes).
Ahlgren, Scott; Ono, Ken; Congruence properties for the partition function. Proc. Natl. Acad. Sci. USA 98 (2001), no. 23, 12882–12884. (doi, MR, notes).
Aigner, Martin; Ziegler, Günter M.; Proofs from The Book. Sixth edition. Including illustrations by Karl H. Hofmann, Springer, Berlin, 2018. viii+326 pp. ISBN: 978-3-662-57264-1, ISBN: 978-3-662-57265-8. (doi, MR, notes).
Akande, A. P.; Genao, Tyler; Haag, Summer; Hendon, Maurice D.; Pulagam, Neelima; Schneider, Robert; Sills, Andrew V.; Computational study of non-unitary partitions.; J. Ramanujan Math. Soc. 38 (2023), no. 2, 121–128. (doi, arxiv, MR, notes).
Alaca, Şaban; Williams, Kenneth S.; Introductory algebraic number theory. Cambridge University Press, Cambridge, 2004. xviii+428 pp. ISBN:0-521 ISBN:0-521-54011-9 (doi, MR, notes).
Alfes, Claudia; Jameson, Marie; Lemke Oliver, Robert J.; Proof of the Alder-Andrews conjecture. Proc. Amer. Math. Soc. 139 (2011), no. 1, 63–78. (doi, MR, notes)
Almkvist, Gert; Partitions with parts in a finite set and with parts outside a finite set. Experiment. Math. 11 (2002), no. 4, 449–456. (link, MR, notes).
Amoroso, Francesco; Viada, Evelina; Small points on subvarieties of a torus. Duke Math. J. 150 (2009), no. 3, 407–442. (doi, MR, notes).
Anderson, Theresa C.; Rolen, Larry; Stoehr, Ruth; Benford's law for coefficients of modular forms and partition functions. Proc. Amer. Math. Soc. 139 (2011), no. 5, 1533–1541. (doi, MR, notes).
Andrews, George E. The theory of partitions. Encyclopedia Math. Appl., Vol. 2 Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. xiv+255 pp. (doi, MR, notes).
Andrews, George E.; Eriksson, Kimmo; Integer partitions. Cambridge University Press, Cambridge, 2004. x+141 pp. (doi, notes).
Apostol, Tom M.; Introduction to analytic number theory. Undergrad. Texts Math. Springer-Verlag, New York-Heidelberg, 1976. xii+338 pp. (doi, notes).
Atiyah, M. F.; Macdonald, I. G.; Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. ix+128 pp. (doi, MR, notes).
Awtrey, Chad; Dodecic 3-adic fields. Int. J. Number Theory 8 (2012), no. 4, 933–944. (doi, MR, notes).
Awtrey, Chad; Barkley, Brett; Miles, Nicole E.; Shill, Christopher; Strosnider, Erin; Degree 12 2-adic fields with automorphism group of order 4. Rocky Mountain J. Math. 45 (2015), no. 6, 1755–1764. (doi, MR, notes).
Awtrey, Chad; Miles, Nicole; Milstead, Jonathan; Shill, Christopher; Strosnider, Erin; Degree 14 2-adic fields. Involve 8 (2015), no. 2, 329–336. (doi, MR, notes).
Ayoub, Raymond; An introduction to the analytic theory of numbers. Math. Surveys, No. 10 American Mathematical Society, Providence, RI, 1963. xiv+379 pp. (doi, notes).
Bajpai, Prajeet; Bennett, Michael A.; Effective $S$-unit equations beyond three terms: Newman's conjecture. Acta Arith. 214 (2024), 421–458. (doi, MR, arxiv, notes).
Baker, A. Linear forms in the logarithms of algebraic numbers. I, II, III. Mathematika 13 (1966), 204–216; ibid. 14 (1967), 102–107; ibid. 14 (1967), 220–228. (doi, MR, notes).
Baker, A.; Wüstholz, G. Logarithmic forms and group varieties. J. Reine Angew. Math. 442 (1993), 19–62. (doi, MR, notes).
Banerjee, Koustav; Paule, Peter; Radu, Cristian-Silviu; Schneider, Carsten; Error bounds for the asymptotic expansion of the partition function. Rocky Mountain J. Math. 54 (2024), no. 6, 1551–1592. (doi, MR, arxiv, notes).
Bannai, Etsuko; Positive definite unimodular lattices with trivial automorphism groups. Mem. Amer. Math. Soc. 85 (1990), no. 429, iv+70 pp. (doi, MR, notes).
Barroero, Fabrizio; Frei, Christopher; Tichy, Robert F.; Additive unit representations in rings over global fields—a survey. Publ. Math. Debrecen 79 (2011), no. 3-4, 291–307. (doi, MR, notes).
Belcher, Paul; A test for integers being sums of distinct units applied to cubic fields. J. London Math. Soc. (2) 12 (1975/76), no. 2, 141–148. (doi, MR, notes).
Bell, Jason P.; When structures are almost surely connected. Electron. J. Combin. 7 (2000), Research Paper 36, 7 pp. (doi, notes)
Blomer, Valentin; Kala, Vítězslav; On the rank of universal quadratic forms over real quadratic fields. Doc. Math. 23 (2018), 15–34. (doi, MR, arxiv, notes).
Bremner, Andrew; Guy, Richard K.; Two more representation problems. Proc. Edinburgh Math. Soc. (2) 40 (1997), no. 1, 1–17. (doi, MR, notes).
Bremner, Andrew; Guy, Richard K.; Nowakowski, Richard J.; Which integers are representable as the product of the sum of three integers with the sum of their reciprocals?. Math. Comp. 61 (1993), no. 203, 117–130. (doi, notes)
Bremner, Andrew; Macleod, Allan; An unusual cubic representation problem. Ann. Math. Inform. 43 (2014), 29–41. (link, MR, notes).
Bremner, Andrew; Xuan, Tho Nguyen; The equation $(w+x+y+z)(1/w+1/x+1/y+1/z)=n$. Int. J. Number Theory 14 (2018), no. 5, 1229–1246. (doi, MR, notes).
Brown, Jim L.; Li, Yingkun; Distribution of powers of the partition function modulo $\ell^j$. J. Number Theory 129 (2009), no. 10, 2557–2568. (doi, notes)
Brueggeman, Sharon A.; Integers representable by $(x+y+z)^3/xyz$. Internat. J. Math. Math. Sci. 21 (1998), no. 1, 107–116. (doi, MR, notes).
Brunotte, Horst; The computation of a certain metric invariant of an algebraic number field. Math. Comp. 38 (1982), no. 158, 627–632. (doi, MR, notes).
Brunotte, Horst; Zur Zerlegung totalpositiver Zahlen in Ordnungen totalreeller algebraischer Zahlkörper. [On the decomposition of totally positive numbers in orders of totally real algebraic number fields] Arch. Math. (Basel) 41 (1983), no. 6, 502–503. (doi, MR, notes).
Bugeaud, Yann; Győry, Kálmán; Bounds for the solutions of unit equations. Acta Arith. 74 (1996), no. 1, 67–80. (doi, MR, notes).
Calegari, Frank; Morrison, Scott; Snyder, Noah; Cyclotomic integers, fusion categories, and subfactors. Comm. Math. Phys. 303 (2011), no. 3, 845–896. (doi, MR, notes)
Cassels, J. W. S.; Local fields. London Math. Soc. Stud. Texts, 3, Cambridge University Press, Cambridge, 1986. xiv+360 pp. ISBN:0-521-30484-9 ISBN:0-521-31525-5 (doi, MR, notes).
Cassels, J. W. S. On a conjecture of R. M. Robinson about sums of roots of unity. J. Reine Angew. Math. 238 (1969), 112–131. (doi, MR, notes).
Cassels, J. W. S. Rational quadratic forms. London Math. Soc. Monogr., 13, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1978. xvi+413 pp. ISBN:0-12-163260-1 (doi, MR, notes).
Čech, Martin; Lachman, Dominik; Svoboda, Josef; Tinková, Magdaléna; Zemková, Kristýna; Universal quadratic forms and indecomposables over biquadratic fields. Math. Nachr. 292 (2019), no. 3, 540–555. (doi, MR, notes).
Chan, Wai-kiu; Kim, Myung-Hwan; Raghavan, S.; Ternary universal integral quadratic forms over real quadratic fields. Japan. J. Math. (N.S.) 22 (1996), no. 2, 263–273. (doi, MR, notes).
Chan, Wai Kiu; Oh, Byeong-Kweon; Can we recover an integral quadratic form by representing all its subforms?. Adv. Math. 433 (2023), Paper No. 109317, 20 pp. (doi, MR, notes).
Chen, Shi-Chao; Distribution of the coefficients of modular forms and the partition function. Arch. Math. (Basel) 98 (2012), no. 4, 307–315. (doi, MR, notes).
Childress, Nancy; Class field theory. Universitext, Springer, New York, 2009. x+226 pp. ISBN:978-0-387-72489-8. (doi, MR, notes).
Cho, Sungmun; Group schemes and local densities of quadratic lattices in residue characteristic 2. Compos. Math. 151 (2015), no. 5, 793–827. (doi, MR, notes).
Choi, Dohoon; Lee, Youngmin; Newman's conjecture for the partition function modulo integers with at least two distinct prime divisors. Adv. Math. 477 (2025), Paper No. 110367, 33 pp. (doi, MR, notes).
Cilleruelo, Javier; Luca, Florian; On the largest prime factor of the partition function of $n$. Acta Arith. 156 (2012), no. 1, 29–38. (doi, link, MR, notes).
Cohen, Henri; A course in computational algebraic number theory. Grad. Texts in Math., 138, Springer-Verlag, Berlin, 1993. xii+534 pp. ISBN:3-540-55640-0. (doi, MR, notes).
Cohen, Henri; Advanced topics in computational number theory. Grad. Texts in Math., 193 Springer-Verlag, New York, 2000. xvi+578 pp. ISBN:0-387-98727-4. (doi, MR, notes).
Cohen, H.; Lenstra, H. W., Jr.; Heuristics on class groups of number fields. Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), 33–62. Lecture Notes in Math., 1068, Springer-Verlag, Berlin, 1984, ISBN:3-540-13356-9 (doi, MR, notes).
Cohen, Henri; Roblot, Xavier-François; Computing the Hilbert class field of real quadratic fields. Math. Comp. 69 (2000), no. 231, 1229–1244. (doi, MR, notes).
Collins, Michael J. On Jordan's theorem for complex linear groups. J. Group Theory 10 (2007), no. 4, 411–423. (doi, MR, notes).
Comtet, Louis; Advanced combinatorics. The art of finite and infinite expansions. Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. xi+343 pp. ISBN: 90-277-0441-4 (doi, MR, notes).
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; Wilson, R. A. ATLAS of finite groups. Maximal subgroups and ordinary characters for simple groups. With computational assistance from J. G. Thackray, Oxford University Press, Eynsham, 1985. xxxiv+252 pp. ISBN: 0-19-853199-0 (doi, MR, notes).
Conway, J. H.; Sloane, N. J. A.; Sphere packings, lattices and groups. Third edition. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov, Grundlehren Math. Wiss., 290 [Fundamental Principles of Mathematical Sciences] Springer-Verlag, New York, 1999. lxxiv+703 pp. ISBN:0-387-98585-9 (doi, MR, notes).
Cornell, Gary; Rosen, Michael; A note on the splitting of the Hilbert class field. J. Number Theory 28 (1988), no. 2, 152–158. (doi, MR, notes).
Cox, David A.; Primes of the form $x^2+ny^2$ — Fermat, class field theory, and complex multiplication. Third edition with solutions. With contributions by Roger Lipsett. AMS Chelsea Publishing, Providence, RI, [2022], ©2022. xv+533 pp. ISBN:9781470470289 ISBN:[9781470471835. (doi, MR, notes).
Cramér, H. On the order of magnitude of the difference between consecutive prime numbers. Acta Arith. 2, 23-46 (1936). (doi, link, ZB, notes).
Cusick, T. W.; Lower bounds for regulators. Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), 63–73. Lecture Notes in Math., 1068 Springer-Verlag, Berlin, 1984 ISBN:3-540-13356-9. (doi, MR, notes).
Dai, Haobo; Fang, Xianwen; On the distribution of the coefficients of modular forms modulo $p^j$. Proc. Amer. Math. Soc. 145 (2017), no. 4, 1415–1419. (doi, MR, notes)
Darmon, Henri; Rational points on curves. Arithmetic geometry, 7–53. Clay Math. Proc., 8, American Mathematical Society, Providence, RI, 2009 ISBN:978-0-8218-4476-2 (doi, MR, notes).
de Bruijn, N. G.; Asymptotic methods in analysis. Second edition, Bibl. Math., Vol. IV [Mathematics Library], North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen, 1961. xii+200 pp. (doi, MR, notes).
Dickson, L. E.; Ternary quadratic forms and congruences. Ann. of Math. (2) 28 (1926/27), no. 1-4, 333–341. (doi, MR, notes).
Dress, Andreas; Scharlau, Rudolf; Indecomposable totally positive numbers in real quadratic orders. J. Number Theory 14 (1982), no. 3, 292–306. (doi, MR, notes).
Dummit, David S.; Voight, John; The 2-Selmer group of a number field and heuristics for narrow class groups and signature ranks of units. Proc. Lond. Math. Soc. (3) 117 (2018), no. 4, 682–726. (doi, MR, notes).
Earnest, A. G.; Universal and regular positive quadratic lattices over totally real number fields. Integral quadratic forms and lattices (Seoul, 1998), 17–27. Contemp. Math., 249, American Mathematical Society, Providence, RI, 1999. ISBN:0-8218-1949-6 (doi, MR, notes).
Eisenstein, G. Tabelle der reducirten positiven ternären quadratischen Formen, nebst den Resultaten neuer Forschungen über diese Formen, in besonderer Rücksicht auf ihre tabellarische Berechnung. J. Reine Angew. Math. 41 (1851), 141–190. (doi, zenodo, MR, notes).
Elkies, Noam D.; Kane, Daniel M.; Kominers, Scott Duke; Minimal $S$-universality criteria may vary in size. J. Théor. Nombres Bordeaux 25 (2013), no. 3, 557–563. (doi, MR, notes).
Elsner, C.; On a sequence transformation with integral coefficients for Euler's constant. Proc. Amer. Math. Soc. 123 (1995), no. 5, 1537–1541. (doi, MR, notes).
Erdős, Paul; Ivić, Aleksandar; The distribution of values of a certain class of arithmetic functions at consecutive integers. Number theory, Vol. I (Budapest, 1987), 45–91. Colloq. Math. Soc. János Bolyai, 51, North-Holland Publishing Co., Amsterdam, 1990 (doi, MR, link, notes).
Erdős, Paul; Ko, Chao; On definite quadratic forms, which are not the sum of two definite or semi-definite forms. Acta Arith. 3 (1938), 102–122. (doi, MR, ZB, notes).
Erdős, P.; Nicolas, J.-L.; Sárközy, A.; On the number of partitions of $n$ without a given subsum. I. Graph theory and combinatorics (Cambridge, 1988) Discrete Math. 75 (1989), no. 1-3, 155–166. (doi, MR, notes).
Erdős, P.; Nicolas, J.-L.; Sárközy, A.; On the number of partitions of $n$ without a given subsum. II. Analytic number theory (Allerton Park, IL, 1989), 205–234. Progr. Math., 85, Birkhäuser Boston, Inc., Boston, MA, 1990. ISBN: 0-8176-3481-9 (doi, MR, notes).
Evertse, Jan-Hendrik; Győry, Kálmán; Unit equations in Diophantine number theory. Cambridge Stud. Adv. Math., 146, Cambridge University Press, Cambridge, 2015. xv+363 pp. ISBN:978-1-107-09760-5. (doi, MR, notes).
Evertse, Jan-Hendrik; Győry, Kálmán; Discriminant equations in Diophantine number theory. New Math. Monogr., 32, Cambridge University Press, Cambridge, 2017. xviii+457 pp. ISBN:978-1-107-09761-2 (doi, MR, notes).
Evertse, J.-H.; Győry, K.; Stewart, C. L.; Tijdeman, R.; S-unit equations and their applications. New advances in transcendence theory (Durham, 1986), 110–174. Cambridge University Press, Cambridge, 1988 ISBN:0-521-33545-0 (doi, MR, notes).
Feit, Walter; Orders of finite linear groups. Proceedings of the First Jamaican Conference on Group Theory and its Applications (Kingston, 1996), 9–11. University of the West Indies, Mona Campus, Kingston, [1996]. (doi, MR, notes).
Finch, Steven R. Mathematical constants. Encyclopedia Math. Appl., 94 Cambridge University Press, Cambridge, 2003. xx+602 pp. (doi, MR, notes).
Finch, Steven R.; Mathematical constants. II. Encyclopedia Math. Appl., 169 Cambridge University Press, Cambridge, 2019. xii+769 pp. (doi, MR, notes).
Flajolet, Philippe; Sedgewick, Robert; Analytic combinatorics. Cambridge University Press, Cambridge, 2009. xiv+810 pp. ISBN: 978-0-521-89806-5 (doi, MR, notes).
Fontaine, Jean-Marc; Il n'y a pas de variété abélienne sur Z. [There are no abelian varieties over Z] Invent. Math. 81 (1985), no. 3, 515–538. (doi, MR, notes).
Fouvry, Étienne; Klüners, Jürgen; On the negative Pell equation. Ann. of Math. (2) 172 (2010), no. 3, 2035–2104. (doi, MR, notes).
Freitas, Nuno; Kraus, Alain; Siksek, Samir; The unit equation over cyclic number fields of prime degree. Algebra Number Theory 15 (2021), no. 10, 2647–2653. (doi, MR, notes).
Friedland, Shmuel, The maximal orders of finite subgroups in $\text{GL}_n(\mathbb{Q})$, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3519–3526. (doi, MR, notes).
Fuchs, Clemens; Tichy, Robert; Ziegler, Volker; On quantitative aspects of the unit sum number problem. Arch. Math. (Basel) 93 (2009), no. 3, 259–268. (doi, MR, notes).
Gajdzica, Krystian; Restricted partition functions and the $r$-log-concavity of quasi-polynomial-like functions. Acta Arith. 217 (2025), no. 1, 67–94. (doi, MR, notes).
Gan, Wee Teck; Yu, Jiu-Kang; Group schemes and local densities. Duke Math. J. 105 (2000), no. 3, 497–524. (doi, MR, notes).
Gil-Muñoz, Daniel; Tinková, Magdaléna; Additive structure of non-monogenic simplest cubic fields. Ramanujan J. 66 (2025), no. 3, Paper No. 47, 56 pp. (doi, MR, notes).
Glaisher, J. W. L. On the number of partitions of a number into a given number of parts. Quart. J. 40, 57-143 (1908). (doi, ZB, notes).
Gorenstein, Daniel; Lyons, Richard; Solomon, Ronald; The classification of the finite simple groups. Math. Surveys Monogr., 40.1, American Mathematical Society, Providence, RI, 1994. xiv+165 pp. ISBN: 0-8218-0334-4 (doi, MR, notes).
Graham, S. W.; Kolesnik, G.; van der Corput's method of exponential sums. London Math. Soc. Lecture Note Ser., 126, Cambridge University Press, Cambridge, 1991. vi+120 pp. ISBN:0-521-33927-8. (doi, MR, notes).
Guàrdia Rúbies, J., Jones, J. W., Keating, K., Pauli, S., Roberts, D. P., & Roe, D. (2025). Families of p-adic fields. arXiv e-prints, arXiv-2507. (arxiv, notes).
Hajdu, L.; A quantitative version of Dirichlet's $S$-unit theorem in algebraic number fields. Publ. Math. Debrecen 42 (1993), no. 3-4, 239–246. (doi, MR, notes).
Hardy, G. H.; Ramanujan, S. Asymptotic Formulæ in Combinatory Analysis. Proc. London Math. Soc. (2) 17 (1918), 75–115. (doi, MR, notes).
Hasse, Helmut; Zahlentheorie. (German) Dritte berichtigte Auflage, Akademie-Verlag, Berlin, 1969. xvi+611 pp. (doi, MR, notes).
Hejda, Tomáš; Kala, Vítězslav; Additive structure of totally positive quadratic integers. Manuscripta Math. 163 (2020), no. 1-2, 263–278. (doi, MR, notes).
Herstein, I. N. Topics in ring theory. University of Chicago Press, Chicago, Ill.-London, 1969. xi+132 pp. (doi, MR, notes).
Hilgart, Tobias; Ziegler, Volker; Twisted Thue equations with multiple exponents in fixed number fields. J. Théor. Nombres Bordeaux 36 (2024), no. 2, 621–635. (doi, MR, notes).
Hirschfeld, J. W. P.; Linear codes and algebraic curves. Geometrical combinatorics (Milton Keynes, 1984), 35–53. Res. Notes in Math., 114 Pitman (Advanced Publishing Program), Boston, MA, 1984. (doi, MR, notes).
Hoshi, Akinari; On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields. J. Number Theory 131 (2011), no. 11, 2135–2150. (doi, MR, notes).
Hoshi, Akinari; Miyake, Katsuya; A note on the field isomorphism problem of $X^3+sX+s$ and related cubic Thue equations. Interdiscip. Inform. Sci. 16 (2010), no. 1, 45–54. (doi, MR, notes).
Hou, Xiang-Dong; Keating, Kevin; Enumeration of isomorphism classes of extensions of p-adic fields. J. Number Theory 104 (2004), no. 1, 14–61. (doi, MR, notes).
Hsia, J. S.; Icaza, M. I.; Effective version of Tartakowsky's theorem. Acta Arith. 89 (1999), no. 3, 235–253. (doi, MR, notes).
Hsia, John S.; Kitaoka, Yoshiyuki; Kneser, Martin; Representations of positive definite quadratic forms. J. Reine Angew. Math. 301 (1978), 132–141. (doi, MR, notes).
Humbert, Pierre; Réduction de formes quadratiques dans un corps algébrique fini. Comment. Math. Helv. 23 (1949), 50–63. (doi, notes).
Icaza, María Inés; Sums of squares of integral linear forms. Acta Arith. 74 (1996), no. 3, 231–240. (doi, MR, notes).
Ireland, Kenneth; Rosen, Michael; A classical introduction to modern number theory. Second edition, Grad. Texts in Math., 84, Springer-Verlag, New York, 1990. xiv+389 pp. ISBN:0-387-97329-X (doi, MR, notes).
Jacobson, Michael J., Jr.; Lukes, Richard F.; Williams, Hugh C.; An investigation of bounds for the regulator of quadratic fields. Experiment. Math. 4 (1995), no. 3, 211–225. (link, MR, notes).
Jang, Se Wook; Kim, Byeong Moon; A refinement of the Dress-Scharlau theorem. J. Number Theory 158 (2016), 234–243. (doi, MR, notes).
Jarden, Moshe; Narkiewicz, Władysław; On sums of units. Monatsh. Math. 150 (2007), no. 4, 327–332. (doi, MR, notes).
Jones, John W.; Roberts, David P. A database of local fields. J. Symbolic Comput. 41 (2006), no. 1, 80–97. (doi, MR, notes).
Jones, John W.; Roberts, David P. Octic 2-adic fields. J. Number Theory 128 (2008), no. 6, 1410–1429. (doi, MR, notes).
Kala, Vítězslav; Norms of indecomposable integers in real quadratic fields. J. Number Theory 166 (2016), 193–207. (doi, MR, notes).
Kala, Vítězslav; Universal quadratic forms and indecomposables in number fields: a survey. Commun. Math. 31 (2023), no. 2, 81–114. (doi, MR, notes).
Kala, Vítězslav; Krásenský, Jakub; Romeo, Giuliano; Universality criterion sets for quadratic forms over number fields, arXiv:2410.22507 [math.NT] (arxiv).
Kala, Vítězslav; Man, Siu Hang; Sails for universal quadratic forms. Selecta Math. (N.S.) 31 (2025), no. 2, Paper No. 26, 31 pp. (doi, MR, notes).
Kala, Vítězslav; Sgallová, Ester; Tinková, Magdaléna; Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables. J. Number Theory 273 (2025), 37–95. (doi, MR, notes).
Kala, Vítězslav; Svoboda, Josef; Universal quadratic forms over multiquadratic fields. Ramanujan J. 48 (2019), no. 1, 151–157. (doi, MR, notes).
Kala, Vítězslav; Tinková, Magdaléna; Universal quadratic forms, small norms, and traces in families of number fields. Int. Math. Res. Not. IMRN 2023, no. 9, 7541–7577. (doi, MR, notes).
Kala, Vítězslav; Yatsyna, Pavlo; Lifting problem for universal quadratic forms. Adv. Math. 377 (2021), Paper No. 107497, 24 pp. (doi, MR, notes).
Kala, Vítězslav; Yatsyna, Pavlo; On Kitaoka's conjecture and lifting problem for universal quadratic forms. Bull. Lond. Math. Soc. 55 (2023), no. 2, 854–864. (doi, MR, notes).
Kala, Vítězslav; Zindulka, Mikuláš; Partitions into powers of an algebraic number. Ramanujan J. 64 (2024), no. 2, 537–551. (doi, MR, notes).
Kaplansky, Irving; Commutative rings. Revised edition, University of Chicago Press, Chicago, Ill.-London, 1974. ix+182 pp. (doi, MR, notes).
Karpenkov, Oleg N.; Geometry of continued fractions. Second edition; Algorithms Comput. Math., 26, Springer, Berlin, [2022], ©2022. xx+451 pp. ISBN:978-3-662-65276-3; ISBN:978-3-662-65277-0 (doi, MR, notes).
Kellner, Bernd C.; On asymptotic constants related to products of Bernoulli numbers and factorials. Integers 9 (2009), A8, 83–106. (doi, arxiv, MR, notes).
Kim, Byeong Moon; Universal octonary diagonal forms over some real quadratic fields. Comment. Math. Helv. 75 (2000), no. 3, 410–414. (doi, MR, notes).
Kim, Byeong Moon; Kim, Myung-Hwan; Oh, Byeong-Kweon; 2-universal positive definite integral quinary quadratic forms. Integral quadratic forms and lattices (Seoul, 1998), 51–62. Contemp. Math., 249 American Mathematical Society, Providence, RI, 1999. (doi, MR, notes).
Kim, Byeong Moon; Kim, Myung-Hwan; Oh, Byeong-Kweon; A finiteness theorem for representability of quadratic forms by forms. J. Reine Angew. Math. 581 (2005), 23–30. (doi, MR, notes).
Kim, B. M.; Kim, M.-H.; Raghavan, S.; 2-universal positive definite integral quinary diagonal quadratic forms. International Symposium on Number Theory (Madras, 1996) Ramanujan J. 1 (1997), no. 4, 333–337. (doi, MR, notes).
Kim, Myung-Hwan; Recent developments on universal forms. Algebraic and arithmetic theory of quadratic forms, 215–228. Contemp. Math., 344, American Mathematical Society, Providence, RI, 2004. ISBN:0-8218-3441-X (doi, MR, notes).
Kim, Kyoungmin; Lee, Jeongwon; Oh, Byeong-Kweon; Minimal universality criterion sets on the representations of binary quadratic forms. J. Number Theory 238 (2022), 37–59. (doi, MR, notes).
Kitaoka, Yoshiyuki; Arithmetic of quadratic forms. Cambridge Tracts in Math., 106 Cambridge University Press, Cambridge, 1993. x+268 pp. (doi, MR, notes).
Ko, Chao; On the representation of a quadratic form as a sum of squares of linear forms. Quart. J. Math. Oxford Ser. 8 (1937), 81–98. (doi, MR, ZB, notes).
Komatsu, Toru, Pairs of cyclic cubic units with rational difference. Int. J. Number Theory 21 (2025), no. 1, 35–52. 2024 (doi, MR, notes).
Kominers, Scott Duke; Uniqueness of the 2-universality criterion. Note Mat. 28 (2008), no. 2, 203–206. (doi, MR, notes).
Kominers, Scott Duke; Oh's 8-universality criterion is unique. Kyungpook Math. J. 61 (2021), no. 3, 455–459. (doi, MR, notes).
Korner, O. Formeln für die p-adischen Maße der quadratischen Einheitsformen in algebraischen Zahlkörpern, Math. Ann. 200 (1973), 267–279. (doi, notes).
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Proceedings:

Integral quadratic forms and lattices. Proceedings of the International Conference held at Seoul National University, Seoul, June 15–19, 1998. Edited by Myung-Hwan Kim, John S. Hsia, Yoshiyuki Kitaoka and Rainer Schulze-Pillot Contemp. Math., 249, American Mathematical Society, Providence, RI, 1999. x+302 pp. ISBN:0-8218-1949-6 (doi, MR, ZB, notes).