Hall 123

Euler-Kronecker constants

S.Jyothsana

CMI, Chennai

In 2006, Ihara introduced and studied Euler-Kronecker constants of
number fields. In particular he made some conjectures about the values of these
constants for cyclotomic fields. Some of these conjectures have been shown to be
false but there is evidence to support some others. We will talk about a conjecture
on the upper bound for the absolute value of the Euler Kronecker constant of a
cyclotomic field. We will also discuss known results in support of this conjecture
and introduce our results in an analogous setup. This is joint work with N. Kandhil
and R. Lunia