On the invariants of L-functions of degree 2, I: twisted degree and internal shift

J. Kaczorowski; A. Perelli

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arXiv · 2405.03186

On the invariants of L-functions of degree 2, I: twisted degree and internal shift

J. Kaczorowski·A. Perelli

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Abstract

This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain unchanged under twist. The ultimate goal of the series is to prove a general version of Weil converse theorem with minimal assumptions on the shape of the functional equation of the twists.

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J. Kaczorowski, A. Perelli. 2024-05-06. On the invariants of L-functions of degree 2, I: twisted degree and internal shift. https://arxiv.org/abs/2405.03186

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