论文标题
具有对数多项式期间功能和算术身份的自动形成积分
Automorphic Integrals with Log-polynomial Period Functions and Arithmetical Identities
论文作者
论文摘要
基于S. Bochner在模块化关系与与Dirichlet系列相关的功能方程的等效性的基础上，K。Chandrasekharan和R. Narasimhan在功能方程与某些算术身份之间获得了新的等价。安·M·希思姐妹（Ann M. Heath）考虑了霍金斯（Hawkins）和诺普（Knopp）上下文中的功能方程，并显示了与整个模块化尖端积分相关的两个算术身份，涉及整个模块化组的合理周期函数。在本文中，我们使用Chandrasekharan和Narasimhan的技术，并将Ann M. Heath姐妹的结果扩展到涉及离散Hecke组合理期间功能的整个自动形态积分。此外，我们建立了两个算术身份的等效性，具有与Hecke组上涉及对数多项式 - period函数的自动形式相关的功能方程。
Building on the works of S. Bochner on equivalence of modular relation with functional equation associated to the Dirichlet series, K. Chandrasekharan and R. Narasimhan obtained new equivalences between the functional equation and some arithmetical identities. Sister Ann M. Heath considered the functional equation in the Hawkins and Knopp context and showed its equivalence to two arithmetical identities associated with entire modular cusp integrals involving rational period functions for the full modular group. In this paper we use techniques of Chandrasekharan and Narasimhan and extend the results of Sister Ann M. Heath to entire automorphic integrals involving rational period functions on discrete Hecke group. Moreover, we establish equivalence of two arithmetical identities with a functional equation associated with automorphic integrals involving log-polynomial-period functions on the Hecke groups.
