Fourier coefficients of Jacobi Poincaré series and applications

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-24 DOI:10.1016/j.jmaa.2024.128994

Abhash Kumar Jha, Animesh Sarkar

引用次数: 0

Abstract

We define Jacobi Poincaré series over Cayley numbers and explicitly compute its Fourier coefficients. As an application, we obtain an estimate for the Fourier coefficients of a Jacobi cusp form. We also evaluate certain Petersson scalar products involving Jacobi cusp forms and Poincaré series. This evaluation yields certain special values of shifted convolution of Dirichlet series of Rankin-Selberg type associated to Jacobi cusp forms in consideration.

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雅可比波恩卡列的傅里叶系数及其应用

我们定义了凯利数上的雅可比庞加莱数列，并明确计算了其傅里叶系数。作为一种应用，我们得到了雅可比凹凸形式傅里叶系数的估计值。我们还评估了涉及雅可比凹凸形式和波恩卡列数列的某些彼得森标量积。通过评估，我们可以得到与雅可比尖顶形式相关的兰金-塞尔伯格类型的移位卷积的某些特殊值。

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.