关于对称幂 L-函数的 Siegel 零点
数论
2023-01-24 v2
摘要
设 为模群 的偶权 全纯尖形式，并假定其为所有 Hecke 算子的公共特征函数。对正整数 ，令 为 的第 次对称幂提升，Newton 与 Thorne 已证明其为自守且尖的。本文利用上述函子性结果，构造若干辅助 -函数，对给定的每个 证明 的 Siegel 零点不存在。作为应用，我们给出了那些对称幂 -函数在 处对数幂型下界。
引用
@article{arxiv.2301.07869,
title = {On Siegel Zeros of Symmetric Power L-functions},
author = {Shifan Zhao},
journal= {arXiv preprint arXiv:2301.07869},
year = {2023}
}
备注
The author was notified that Theorem 1.1 in this note was obtained by Jesse Thorner in his 2021 paper "Effective forms of the Sate-Tate conjecture". The author was not aware of this when he posted it on arXiv. Therefore, the author does not intend to submit this note for publication