E-mail address: Nuno.Arala-Santos(at)warwick.ac.uk.
Number Theory, especially interactions between Analytic Number Theory and Diophantine Geometry.
I obtained my Bachelor's degree from the University of Porto in 2018. I then did my Master's at the University of Bonn, which I finished in 2020. I wrote my Master's Thesis under the supervision of Prof. Valentin Blomer on an analytic approach, based on a variant of the Hardy-Littlewood circle method, to the computation of Representation Numbers of Quadratic Forms. (For more details see below, under "Writing".)
For more information on my background see my CV.
Papers and Preprints
- Lines of polynomials with alternating Galois group (arXiv, .pdf), submitted in May 2022.
- On the density of a set of primes associated to an Elliptic Curve (arXiv, .pdf), to appear in Journal of Number Theory.
Below are some math-related texts I wrote over the years, for various purposes. Several of them are written in Portuguese. I intend to translate some of those to English at some point in the future.
- (2014, in Portuguese) Three handouts on Euclidean Geometry topics, intended for Olympiad students: Geometry for Beginners, Random configurations and Brute Force. These are joint work with Miguel Moreira.
- (2015, in Portuguese) A short handout on the "Lifting the Exponent" Lemma, intended for Olympiad students: Lifting the Exponent.
- (2019, in Portuguese) Affine and Projective Geometry. This text was loosely inspired in a course I took in the final year of my Bachelor's.
- (2020) A short text on the classification of Quaternion Algebras over Local Fields.
- (2020) My Master's Thesis on Representation Numbers of Quadratic Forms.