Unconditional comparative prime number theory over function fields

Speaker: Alexandre Bailleul

Date: Fri, Jun 21, 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


In classical comparative prime number theory, it is customary to assume some kind of linear independence hypothesis about the zeros of the underlying L-functions. These hypotheses are completely out of reach of current methods. However, in the function field case, it is sometimes possible to prove them, or at least to show they hold generically. In this talk I will present recent results in comparative prime number theory over function fields that establish infinite families of “irreducible polynomial races” which we can study unconditionally. Some of those results are joint work with L. Devin, D. Keliher, and W. Li.

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