L-functions in Analytic Number Theory: Alexandre Bailleul

  • Date: 03/22/2023
  • Time: 11:00
Alexandre Bailleul, ENS Paris-Saclay

University of Lethbridge


Exceptional Chebyshev's bias over finite fields


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.

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Time: 11 am Pacific/ 12 pm Mountain


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