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 language | English |
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Pages (from-to) | 93-121 |
Journal | Advanced Studies in Pure mathematics |
Volume | 84 |
DOIs | |
Publication status | Published - Jan 1 2020 |