Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
ON THE RIEMANN HYPOTHESIS FOR A CERTAIN FAMILY OF FORMAL WEIGHT ENUMERATORS
Naoya KANEKOMasakazu YAMAGISHI
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2022 Volume 76 Issue 2 Pages 441-450

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Abstract

A formal weight enumerator is a homogeneous polynomial in two variables which behaves like the Hamming weight enumerator of a self-dual linear code except that the coefficients are not necessarily non-negative integers. Chinen discovered several families of formal weight enumerators and investigated the validity of the Riemann hypothesis analogue for them. In this paper, the zeta polynomial is computed for Chinen's formal weight enumerators, and a simple criterion is given for the validity of the Riemann hypothesis analogue.

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© 2022 Faculty of Mathematics, Kyushu University
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