My research interests lie at the intersection of Analytic Number Theory, Fourier Analysis, and Complex Analysis.
Preprint:
22. A footnote on the integral of the logarithm of the Riemann zeta-function, submitted.
Published papers:
21. Remarks on a formula of Ramanujan, with Steve M. Gonek, to appear in Proceedings of the Royal Society of Edinburgh: Section A.
20. Bounding zeta on the 1‑line under the partial Riemann hypothesis, Bulletin of the Australian Mathematical Society 110 (2024), no. 2, 244–251.
19. An extremal problem and inequalities for entire functions of exponential type, with D. K. Dimitrov, E. Quesada-Herrera and M. Sousa, Proceedings of the American Mathematical Society 152 (2024), no. 8, 3299–3318.
18. Conditional bounds for the logarithmic derivative of Dirichlet L-functions, with A. Simonič and M. Valås Hagen, Indagationes Mathematicae (New Series) 35 (2024), no. 1, 14–27.
17. Point evaluation in Paley-Wiener spaces, with O. F. Brevig, J. Ortega-Cerdà, and K. Seip, Journal d'Analyse Mathématique 153 (2024), no. 2, 595–670.
16. Hilbert spaces and low-lying zeros of L-functions, with E. Carneiro and M. B. Milinovich, Advances in Mathematics 410 (2022), Paper No. 108748.
15. Optimality for the two-parameter quadratic sieve, with E. Carneiro, H. A. Helfgott, and J. Mejía-Cordero, Acta Arithmetica 203 (2022), no. 3, 195–226.
14. On Montgomery's pair correlation conjecture: a tale of three integrals, with E. Carneiro, V. Chandee, and M. B. Milinovich, Journal für die reine un angewandte Mathematik (Crelle's journal) 786 (2022), 205–243.
13. A note on the mean values of the derivatives of ζ'/ζ, Proceedings of the American Mathematical Society 150 (2022), no. 8, 3253–3265.
12. The second moment of Sₙ(t) on the Riemann hypothesis, with E. Quesada-Herrera, International Journal of Number Theory 18 (2022), no. 6, 1203–1226.
11. Fourier optimization and quadratic forms, with E. Quesada-Herrera, Quarterly Journal of Mathematics 73 (2022), no. 2, 539–577.
10. Bounding the log-derivative of the zeta-function, with F. Gonçalves, Mathematische Zeitschrift 300 (2022), no. 1, 1041–1053.
9. A note on the zeros of approximations of the Ramanujan Ξ-function, with O. Velásquez, Ramanujan Journal 57 (2022), no. 1, 389–400.
8. Large oscillations of the argument of the Riemann zeta-function, with K. Mahatab, Bulletin of the London Mathematical Society 53 (2021), 1776–1785.
7. Primes in arithmetic progressions and semidefinite programming, with V. Pereira and D. de Laat, Mathematics of Computation 90 (2021), no. 331, 2235–2246.
6. Large values of the argument of the Riemann-zeta function and its iterates, with K. Mahatab, Journal of Number Theory 225 (2021), 240–259.
5. Pair correlation estimates for the zeros of the zeta function via semidefinite programming, with F. Gonçalves and D. de Laat, Advances in Mathematics 361 (2020), 22 pp.
4. Extreme values for Sₙ(σ,t) near the critical line, Journal of Number Theory 200 (2019), 329–352.
3. A note on Entire L-functions, Bulletin of the Brazilian Mathematical Society (N.S.) 50 (2019), no. 1, 67–93.
2. Bandlimited approximations and estimates for the Riemann zeta-function, with E. Carneiro and M. B. Milinovich, Publicacions Matemàtiques 63 (2019), no. 2, 601–661.
1. Bounding Sₙ(t) on the Riemann hypothesis, with E. Carneiro, Mathematical Proceedings of the Cambridge Philosophical Society 164 (2018), 259–283.