# On generalized Brauer-Siegel theorem and the Euler-Kronecker constants

## Meeting Details

Abstract: For a number field $K$, let $h_K$ denote the class number. It is an important theme in number theory to understand how $h_K$ varies over a family of number fields. In this context, the classical Brauer-Siegel theorem describes how the class number times the regular varies over Galois fields $K/\mathbb{Q}$. An analogue of this statement for more general families was conjectured by Tsfasman and Vladut in 2002. On another front, as a natural generalization of Euler's constant $\gamma$, Ihara introduced the Euler-Kronecker constant attached to any number field $K$. In this talk, we will discuss a connection between the generalized Brauer-Siegel conjecture and bounds on the Euler-Kronecker constant, proving the Brauer-Siegel conjecture in some special cases.