The standard twist of -functions revisited
Volume 201 / 2021
Acta Arithmetica 201 (2021), 281-328
MSC: Primary 11M41.
DOI: 10.4064/aa210730-23-8
Published online: 24 November 2021
Abstract
The analytic properties of the standard twist F(s,\alpha ), where F(s) belongs to a wide class of L-functions, are of prime importance in describing the structure of the Selberg class. In this paper we present a deeper study of such properties. In particular, we show that F(s,\alpha ) satisfies a functional equation of a new type, somewhat resembling that of the Hurwitz–Lerch zeta function. Moreover, we detect the finer polar structure of F(s,\alpha ), characterizing in two different ways the occurrence of finitely or infinitely many poles as well as giving a formula for their residues.
