Research

I am interested in the applications of multiple Dirichlet series in analytic number theory and in the interaction between the classical and multiple Dirichlet series approach to problems such as moments of L-functions.

Publications:

1.   Moments of real Dirichlet $L$-functions and multiple Dirichlet series, submitted. Arxiv. 

2. (with K. Matomäki) A note on exceptional characters and non-vanishing of Dirichlet L-functions (2023), Math. Ann.. Journal. Arxiv.

3.  Ratios conjecture and multiple Dirichlet series (2024), Trans. Amer. Math. Soc. 377, 3487--3528. Journal. Arxiv.

4.  Mean value of real characters using a double Dirichlet series (2023), Canadian Math. Bull. 66(4) : 1135-1151. Journal.  Arxiv.

5.  (with D. Lachman, J. Svoboda, M. Tinková, K. Zemková), Universal quadratic forms and indecomposables over biquadratic fields (2019), Math. Nachr. 292 (3), 540--555.  Journal. Arxiv.

• (doctoral thesis, 2022) Applications of multiple Dirichlet series in analytic number theory. Link.

Talks and presentations:

• Canadian Mathematical Society Winter meeting. Ratios conjecture and multiple Dirichlet series (December 2021). Slides. 

• Stanford University, Learning Analytic Number Theory Seminar (November 2021). Ratios conjectures and multiple Dirichlet series. Slides.

• Ratios conjectures and multiple Dirichlet series. Number theory seminar at UC Irvine (November 2021). Slides.

• Ratios conjecture, one-level density and multiple Dirichlet series. Montréal Online Biweekly Inter-University Seminar on Analytic Number Theory (July 2021).

• A double sum of Jacobi symbols and double Dirichlet series,  University of Bristol Linfoot Seminar (May 2021).

• Multiple Dirichlet series and a double sum of Jacobi symbols, Number Theory seminar at Charles University (April 2021). Slides. Recording.

• Mean values of real Dirichlet characters and a double Dirichlet series, Canadian Mathematical Society Winter meeting (December 2020) Recording. Slides.

• One-level density and the Ratios conjecture, Virtual Learning Analytic Number Theory Seminar in Montréal (October 2020). Slides.

• Double Dirichlet series and a double character sum, Virtual Learning Analytic Number Theory Seminar in Montréal (May 2020). Slides.

• The sieve of Eratosthenes and twin primes,  Number theory seminar at Charles University (2019).

• The cubic sieve, Analytic number theory learning seminar in Montreal (2019).

Here is my Master's thesis about the pretentious approach to analytic number theory.

Here is my Bachelor's thesis about algebraic proofs of Dirichlet's Theorem on primes in arithmetic progressions.