Title

On the nature of e^γ and non-vanishing of derivatives of L-series at s=1/2

Authors

M. Ram Murty, Queen’s University
Naomi Tanabe, Queen’s University

Document Type

Article

Publication Date

4-30-2014

Abstract

In 2011, M.R. Murty and V.K. Murty [10] proved that if L(s, χD) is the Dirichlet L-series attached a quadratic character χD, and L'(1, χD)=0, then eγ is transcendental. This paper investigates such phenomena in wider collections of L-functions, with a special emphasis on Artin L-functions. Instead of s=1, we consider s=1/2. More precisely, we prove thatexp (L'(1/2,χ)L(1/2,χ)-αγ) is transcendental with some rational number α. In particular, if we have L(1/2, χ)≠0 and L'(1/2, χ)=0 for some Artin L-series, we deduce the transcendence of eγ.

Recommended Citation

Murty, M. Ram and Tanabe, Naomi, "On the nature of e^γ and non-vanishing of derivatives of L-series at s=1/2" (2014). Mathematics Faculty Publications. 68.
https://digitalcommons.bowdoin.edu/mathematics-faculty-publications/68