An explicit prime geodesic theorem for discrete tori and the hypergeometric functions

被引：1

作者：

Yamasaki, Yoshinori ^{[1
]}

机构：

[1] Ehime Univ, Grad Sch Sci & Engn, Bunkyo Cho, Matsuyama, Ehime 7908577, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2018年 / 289卷 / 1-2期

关键词：

Discrete tori; Prime geodesic theorem; Heat kernels on graphs; Lauricella hypergeometric functions; Jacobi polynomials; HEAT KERNELS; CLOSED GEODESICS; HOMOLOGY CLASSES; ZETA-FUNCTIONS;

D O I：

10.1007/s00209-017-1955-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The discrete tori are graph analogues of the real tori, which are defined by the Cayley graphs of a finite product of finite cyclic groups. In this paper, using the theory of the heat kernel on the discrete tori established by Chinta, Jorgenson and Karlsson, we derive an explicit prime geodesic theorem for the discrete tori, which is not an asymptotic formula. To describe the formula, we need generalizations of the classical Jacobi polynomials, which are defined by the Lauricella multivariable hypergeometric function of type C.

引用

页码：361 / 376

页数：16

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