Distribution of Gaussian primes and zeros of L-functions
Speaker: Lucile Devin
Date: Wed, Jun 19, 2024
Location: PIMS, University of British Columbia
Conference: Comparative Prime Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Wed, Jun 19, 2024
Location: PIMS, University of British Columbia
Conference: Comparative Prime Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
In this talk, we are interested in the following question: among primes that can be written as a sum of two squares $p = a^2 + 4b^2$ with $a > 0$, how is the congruence class of a distributed? This will lead us to study the distribution of values of Hecke characters from the point of view of Chebyshev’s bias, as well as the distribution of zeros of the associated L-functions and in particular their vanishing at $1/2$.
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