Euler-Kronecker constants

Ihara defined and began the systematic study of the Euler-Kronecker constant
of a number field. In some cases, these constants arise in the study of periods
of Abelian varieties. For abelian number fields, they can be explicitly connected
to subtle problems about the distribution of primes. In this talk, we review some
known results and describe some joint work with Mariam Mourtada.