Error message

  • Deprecated function: Optional parameter $js declared before required parameter $element is implicitly treated as a required parameter in include_once() (line 1445 of /var/www/html/mathtube.org/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $input declared before required parameter $form_state is implicitly treated as a required parameter in include_once() (line 1445 of /var/www/html/mathtube.org/includes/bootstrap.inc).

The influence of the Galois group structure on the Chebyshev bias in number fields

Speaker: Mounir Hayani

Date: Tue, Jun 18, 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 2020, Fiorilli and Jouve proved an unconditional Chebyshev bias result for a Galois extension of number fields under a group theoretic condition on its Galois group. We extend their result to a larger family of groups. This leads us to characterize abelian groups enabling extreme biases. In the case of prime power degree extensions, we give a simple criterion implying extreme biases and we also investigate the corresponding Linnik-type question.

Additional Files:
PDF icon Hayani.pdf