I am a third year PhD student under the supervision of Dr Adam Harper.

Email: Daniele "dot" Mastrostefano "at" warwick "dot" ac "dot'' uk.

Office: B0.16.

Research Interests:

The distribution of prime numbers, Additive and Multiplicative Number Theory, the elementary approach to Analytic Number Theory, the distribution of arithmetical functions, Sieve Theory, Additive Combinatorics, Probabilistic Number Theory and Metric Number Theory.

Publications and preprints:

• A lower bound for the variance in arithmetic progressions of some multiplicative functions close to 1 (ArXiv preprint).
• The number of representations of an integer as product of two restricted numbers (Note).
• On maximal product sets of random sets (Published, The Journal of Number Theory).
• A lower bound for the variance of generalized divisor functions in arithmetic progressions (Published, The Ramanujan Journal).
• Positive proportion of short intervals containing a prescribed number of primes (Published, Bulletin of Australian Mathematical Society).
• An Upper Bound for the Moments of a G.C.D. related to Lucas Sequences (Published, Rocky Mountain Journal of Mathematics).
• On numbers n with polynomial image coprime with the n-th term of a linear recurrence (Published, Bulletin of the Australian Mathematical Society).
• Short intervals containing a prescribed number of primes (Published, Journal of Number Theory).
• Weighted Average Number of Prime m-tuples lying on an Admissible k-tuple of Linear Forms (Preprint, arXiv version).

Current Research:

This is my main PhD project.

I am also working on large fluctuations of random multiplicative functions together with Adam Harper and on improving the current large deviations results in the Selberg's central limit theorem jointly with Maxim Gerspach. Finally, I am investigating properties of multiplicative Sidon sets with Oleksiy Klurman.

Teaching:

I have been TA for the modules:

• MA257 Introduction to Number Theory (Second term 2019/2020).
• MA258 Mathematical Analysis III (First term 2019/2020).
• MA257 Introduction to Number Theory (Second term 2018/2019).
• MA258 Mathematical Analysis III (First term 2018/2019).

I have been a supervisor for 2 groups of 5 each second year undergraduate students for the modules:

• MA244 Analysis 3 (First term 2018/2019).
• MA251 Algebra 1: Advanced Linear Algebra (First term 2018/2019).
• MA259 Multivariable Calculus (First term 2018/2019).

Activities:

• I gave a talk on ''Maximal random product sets'' during the "NT online conference", virtually held in Turin (18 February 2021).
• Contributed speaker at the "IML Number Theory seminar", virtually held in Stochkolm (8 February 2021).
• I gave a talk about ''A new elementary proof of the Prime Number Theorem'' (University of Warwick, 11 March 2020).
• I took part, giving also some talks, in the study group about "The Duffin&Schaeffer conjecture", held in the University of Warwick.
• Contributed speaker at the WIMP conference, held in the University of Warwick.
• Contributed speaker at the Warwick Y-RANT conference.
• Invited speaker at the 4th Number Theory Meeting Torino.
• I gave a talk on the occasion of the "Speaking with Style" conference, held in the University of Warwick.
• I took part, giving also some talks, in the study group about "Low moments of random multiplicative functions", held in the University of Warwick.
• I started the Mathematical blog A Sequence of IID Random Posts together with Peter Mühlbacher.
• I gave a talk about ''Heuristics for the distribution of primes in short intervals'' (University of Warwick, 23 January 2019).
• I take part in the activities of the Number Theory group at Warwick. During the terms there is a running Seminar as well as a Study group.
• I attended several talks in the context of the Combinatorics Seminar, Probability Seminar and Colloquium.
• I gave a talk on the occasion of The fifth mini symposium of the Roman Number Theory Association about my paper Positive proportion of short intervals containing a prescribed number of primes.

Conferences Attended and Scheduled:

• Number Theory Online (18/02/2021, 24/02/2021, 4/03/2021, Turin).
• Research program in Number Theory at Mittag-Leffler Institute (11/01/2021-26/03/2021, Stockholm; winner of a junior fellowship).
• Nancy Analytic and Probabilistic Number Theory Days (June 2020, Nancy).
• The Duffin and Schaeffer conjecture (December 2019, Bristol).
• Zeta Functions (December 2019, at CIRM).
• Warwick-Imperial Autumn Meeting (November 2019).
• Young researchers in Algebraic and Analytic Number Theory conference (November 2019).
• 4th Number Theory Meeting Torino (October 2019).
• Warwick-Oxbridge-Manchester-Bristol-London (WOMBL) 1-day meeting at Oxford (September 2019).
• Second Symposium on Analytic Number Theory (July 2019).
• Mini-Symposium on "Additive Combinatorics" at the British Combinatorial Conference (July-August 2019).
• The fifth mini symposium of the Roman Number Theory Association (April 2019).
• Warwick-Oxbridge-Manchester-Bristol-London (WOMBL) 1-day meeting at Cambridge (January 2019).
• Warwick-Imperial Autumn Meeting (December 2018).
• The fourth mini symposium of the Roman Number Theory Association (April 2018).
• Giornate INDAM di Teoria dei Numeri (December 2017).

• The third mini symposium of the Roman Number Theory Association (April 2017).

Here is a link to a brief version of my CV, containing information on my previous educational background and awards received.

Here is my Bachelor thesis in Italian: ''The rationality of the Zeta function of algebraic varieties''.

Here is my Master thesis in Italian: ''On recent results about short gaps between consecutive primes''.