Splitting hypergeometric functions over roots of unity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-22 DOI:10.1007/s40687-024-00468-5

Dermot McCarthy, Mohit Tripathi

引用次数: 0

Abstract

We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of unity. We provide multiple applications of these results, including new reduction and summation formulas for finite field hypergeometric functions, along with classical analogues; evaluations of special values of these functions which apply in both the finite field and p-adic settings; and new relations to Fourier coefficients of modular forms.

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在统一根上分割超几何函数

我们研究了有限域、p-adic 和经典环境中的超几何函数。在每种情况下，我们都证明了一个公式，该公式将超几何函数拆分为低阶函数之和，这些低阶函数的参数以同根不同。我们提供了这些结果的多种应用，包括有限域超几何函数的新还原和求和公式以及经典类似公式；适用于有限域和 p-adic 设置的这些函数特殊值的求值；以及与模态的傅里叶系数的新关系。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.