activity
20182021
collaborators

5 papers

math.NT2021

Analytic ranks of automorphic L-functions and Landau-Siegel zeros

Hung M. Bui, Kyle Pratt, Alexandru Zaharescu

We relate the study of Landau-Siegel zeros to the ranks of Jacobians of modular curves for large primes . By a conjecture of Brumer-Murty, the rank should be equal to h…

math.NT2020

Exceptional characters and nonvanishing of Dirichlet -functions

H. M. Bui, Kyle Pratt, Alexandru Zaharescu

Let be a real primitive character modulo . If the -function has a real zero close to , known as a Landau-Siegel zero, then we say the character is excep…

math.NT2018

Dirichlet -functions of quadratic characters of prime conductor at the central point

Siegfred Baluyot, Kyle Pratt

We prove that more than nine percent of the central values are non-zero, where ranges over primes and is the real primitive Dirichle…

math.NT2018

Breaking the -barrier for the twisted second moment of Dirichlet -functions

H. M. Bui, Kyle Pratt, Nicolas Robles +1

We study the second moment of Dirichlet -functions to a large prime modulus twisted by the square of an arbitrary Dirichlet polynomial. We break the -barrier in…

math.NT2018

Primes from sums of two squares and missing digits

Kyle Pratt

Let be the set of integers missing any three fixed digits from their decimal expansion. We produce primes in a thin sequence by proving an asymptotic formula for cou…