Generation of off-critical zeros for hypercubic Epstein zeta functions

作者：

Highlights：

• The generation mechanism of off-critical zeros starting from special critical zeros is revealed for Epstein zeta-functions.

• The exact analysis of the Epstein zeta-functions is made for dimensions going to 0 and to infinity.

• The existence of real off-critical zeros is proved for dimensions larger than 9.24555.

摘要

•The generation mechanism of off-critical zeros starting from special critical zeros is revealed for Epstein zeta-functions.•The exact analysis of the Epstein zeta-functions is made for dimensions going to 0 and to infinity.•The existence of real off-critical zeros is proved for dimensions larger than 9.24555.

论文关键词：Epstein zeta-function,Hypercubic lattice,Analytic continuation,Jacobi theta function,Zeros,Critical phenomena

论文评审过程：Received 4 June 2020, Revised 7 July 2021, Accepted 17 August 2021, Available online 5 September 2021, Version of Record 5 September 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126611