saito-kurokawa举的同余和中心旋量l值的分母

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal Pub Date : 2021-10-14 DOI:10.1017/S0017089521000331

N. Dummigan

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引用次数: 1

摘要

摘要继Ryan和Tornaría之后，我们证明了在Saito-Kurokawa提升和非提升(属2的某些Siegel模形式)之间的Hecke特征值的同余模在非提升的中心旋量l值的分母(除以旋)中出现(平方)。这取决于Böcherer的猜想及其类似物，并在Furusawa, Morimoto和其他人最近的工作背景下进行观察。它需要傅里叶系数的同余，这是从唯一性假设中得到的，或者可以用实例证明。我们通过对Bloch-Kato猜想的仔细检查来解释这些因子的分母。

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CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES

Abstract Following Ryan and Tornaría, we prove that moduli of congruences of Hecke eigenvalues, between Saito–Kurokawa lifts and non-lifts (certain Siegel modular forms of genus 2), occur (squared) in denominators of central spinor L-values (divided by twists) for the non-lifts. This is conditional on Böcherer’s conjecture and its analogues and is viewed in the context of recent work of Furusawa, Morimoto and others. It requires a congruence of Fourier coefficients, which follows from a uniqueness assumption or can be proved in examples. We explain these factors in denominators via a close examination of the Bloch–Kato conjecture.

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来源期刊

Glasgow Mathematical Journal 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics. The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.