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

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-05-06 DOI:10.1142/s1793042124501215

J. Kaczorowski, A. Perelli

引用次数: 0

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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论 2 阶 L 函数的不变式，I：扭曲度与内移

本文是系列论文的第一部分，研究了阶数为 2 的 $L$ 函数在迪里夏特特征扭转下的不变式行为。在此，我们证明，在适当条件下，阶数和内移在扭转下保持不变。这一系列论文的最终目标是证明魏尔反向定理的一般版本，只需对扭转函数方程的形状作最少的假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.