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A problem of Erdős-Graham-Granville-Selfridge on integral points on hyperelliptic curves
Hung M. Bui, Kyle Pratt, Alexandru Zaharescu
Erdős, Graham, and Selfridge considered, for each positive integer , the least value of so that the integers contain a subset the product of whos…
The irrationality of a divisor function series of Erdős and Kac
Kyle Pratt
For positive integers and let denote the sum of the th powers of the divisors of . Erdős and Kac asked whether, for every , the number $α_k = \sum_{n\geq…
Power savings for counting solutions to polynomial-factorial equations
Hung M. Bui, Kyle Pratt, Alexandru Zaharescu
Let be a polynomial with integer coefficients and degree at least two. We prove an upper bound on the number of integer solutions to which yields a power…
Weighted central limit theorems for central values of -functions
Hung M. Bui, Natalie Evans, Stephen Lester +1
We establish a central limit theorem for the central values of Dirichlet -functions with respect to a weighted measure on the set of primitive characters modulo as $q \right…
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…
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…