English

Special values of spectral zeta functions of graphs and Dirichlet L-functions

Number Theory 2023-07-13 v2

Abstract

In this paper, we establish relations between special values of Dirichlet LL-functions and that of spectral zeta functions or LL-functions of cycle graphs. In fact, they determine each other in a natural way. These two kinds of special values were bridged together by a combinatorial derivative formula obtained from studying spectral zeta functions of the first order self-adjoint differential operators on the unit circle.

Keywords

Cite

@article{arxiv.2212.13687,
  title  = {Special values of spectral zeta functions of graphs and Dirichlet L-functions},
  author = {Bing Xie and Yigeng Zhao and Yongqiang Zhao},
  journal= {arXiv preprint arXiv:2212.13687},
  year   = {2023}
}

Comments

2nd version. Minor changes and references updated