Translator Disclaimer
VOL. 84 | 2020 Zeta functions of periodic cubical lattices and cyclotomic-like polynomials
Yasuaki Hiraoka, Hiroyuki Ochiai, Tomoyuki Shirai

Editor(s) Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki

Adv. Stud. Pure Math., 2020: 93-121 (2020) DOI: 10.2969/aspm/08410093

Abstract

Zeta functions of periodic cubical lattices are explicitly derived by computing all the eigenvalues of the adjacency operators and their characteristic polynomials. We introduce cyclotomic-like polynomials to give factorization of the zeta function in terms of them and count the number of orbits of the Galois action associated with each cyclotomic-like polynomial to obtain its further factorization. We also give a necessary and sufficient condition for such a polynomial to be irreducible and discuss its irreducibility from this point of view.

Information

Published: 1 January 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07283183

Digital Object Identifier: 10.2969/aspm/08410093

Subjects:
Primary: 05C50 , 05E45 , 11R09 , 11S40 , 58C40

Keywords: Cubical lattice , cyclotomic-like polynomial , Laplacian , zeta function

Rights: Copyright © 2020 Mathematical Society of Japan

PROCEEDINGS ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
RIGHTS & PERMISSIONS
Get copyright permission
Back to Top