Zeta functions of periodic cubical lattices and Cyclomatic-like polynomials

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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.
Original languageEnglish
Pages (from-to)93-121
JournalAdvanced Studies in Pure mathematics
Volume84
DOIs
Publication statusPublished - Jan 1 2020

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