The standard twist of $L$-functions revisited

نویسندگان

چکیده

The analytic properties of the standard twist $F(s,\alpha)$, where $F(s)$ belongs to a wide class $L$-functions, are prime importance in describing structure Selberg class. In this paper we present deeper study such properties. particular, show that $F(s,\alpha)$ satisfies functional equation new type, somewhat resembling Hurwitz-Lerch zeta function. Moreover, detect finer polar characterizing two different ways occurrence finitely or infinitely many poles as well giving formula for their residues.

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ژورنال

عنوان ژورنال: Acta Arithmetica

سال: 2021

ISSN: ['0065-1036', '1730-6264']

DOI: https://doi.org/10.4064/aa210730-23-8