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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

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

Rights: Copyright © 2020 Mathematical Society of Japan

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