The standard twist of $L$-functions revisited
2021
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.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
0
References
0
Citations
NaN
KQI