Research

My research pivots around Fourier analysis and its connections to number theory.  I have been interested in topics from the uncertainty principle in Fourier analysis, to its relation to Fourier optimization problems that appear in connection with the distribution of integers and primes represented by quadratic forms. I have also studied questions about the Riemann zeta function and other L-functions, such as the distribution of their zeros.

Ph. D. thesis: On uncertainty principles, Fourier optimization and the Riemann zeta-function.

Pre-prints

7. Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression (with E. Carneiro, M. B. Milinovich, and A. P. Ramos), 2024

Papers (published or accepted)

6. An extremal problem and inequalities for entire functions of exponential type (with A. Chirre, D. K. Dimitrov, and Mateus Sousa), Proc. Am. Math. Soc., to appear
5. Generalized sign Fourier uncertainty (with E. Carneiro), Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) Vol. XXIV (2023), 1671-1704.
4. On the number variance of zeta zeros and a conjecture of Berry (with M. M. Lugar and M. B. Milinovich), Mathematika 69, no. 2 (2023), 303-348. [Journal]
3. Fourier optimization and quadratic forms (with A. Chirre), Q. J. Math. 73, no. 2 (2022), 539–577. [Journal]
2. On the q-analogue of the pair correlation conjecture via Fourier optimization, Math. Comp. 91 (2022), 2347-2365 . [Journal]
1. The second moment of Sn(t) on the Riemann Hypothesis (with A. Chirre), Int. J. Number Theory 18, no. 6 (2022), 1203–1226. [Journal]