Tewlede G/Egziabher , Hunduma Legesse Geleta , Abdul Hassen
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引用次数: 1
Abstract
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 to prove results analogous to those of Sister Ann M. Heath. Specifically, we establish equivalence of two arithmetical identities with a functional equation associated with automorphic integrals involving log-polynomial-period functions on the discrete Hecke groups.
K. Chandrasekharan和R. Narasimhan在S. Bochner关于Dirichlet级数的泛函方程与模关系等价的工作的基础上,得到了泛函方程与一些算术恒等式之间的新的等价。Ann M. Heath姐妹考虑了Hawkins和Knopp背景下的泛函方程,并证明了它与全模群中涉及有理周期函数的全模尖积分的两个算术恒等式的等价性。在本文中,我们使用钱德拉塞卡兰和纳拉西姆汉的技术来证明类似于安·m·希思修女的结果。具体地,我们建立了离散Hecke群上涉及对数多项式周期函数的自同构积分的一个泛函方程的两个算术恒等式的等价性。
期刊介绍:
Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.