## L-functions in Analytic Number Theory: Alexandre Bailleul

• Date: 03/22/2023
• Time: 11:00
Lecturer(s):
Alexandre Bailleul, ENS Paris-Saclay
Location:

University of Lethbridge

Topic:

Exceptional Chebyshev's bias over finite fields

Description:

Chebyshev's bias is the surprising phenomenon that there is usually more primes of the form 4n+3 than of the form 4n+1 in initial intervals of the natural numbers. More generally, following work from Rubinstein and Sarnak, we know Chebyshev's bias favours primes that are not squares modulo a fixed integer q compared to primes which are squares modulo q. This phenomenon also appears over finite fields, where we look at irreducible polynomials modulo a fixed polynomial M. However, in the finite field case, there are a few known exceptions to this phenomenon, appearing as a result of multiplicative relations between zeroes of certain L-functions. In this work, we show, improving on earlier work by Kowalski, that those exceptions are rare. This is joint work with L. Devin, D. Keliher and W. Li.

Other Information:

Time: 11 am Pacific/ 12 pm Mountain