Transcendence of Euler-Lehmer constants and values of
L-functions
by
N.Saradha
TIFR, Mumbai
Abstract
In a series of four papers with M. Ram Murty, we obtained several results
onthe arithmetic nature of the values of the classical Digamma, Polygamma
functions at rational points and also on the extended Euler constants defined by Lehmer. Further, the classical L- functions L(s, f ) and its p− adic
analogues are closely related to these functions which enabled us to derive
transcedence results about the values of these functions for certain values of
s. Here f is a periodic function on Z taking algebraic values. These results
depend on an important paper by Baker, Birch and Wirsing based on linear
forms in logarithms. In this talk, I shall give an overview of these results.
1