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arXiv · 1911.10497

The standard twist of L-functions revisited

J. Kaczorowski·A. Perelli
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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.

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J. Kaczorowski, A. Perelli. 2019-11-24. The standard twist of L-functions revisited. https://arxiv.org/abs/1911.10497

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