Formal weight enumerators and Chebyshev polynomials

Yamagishi, Masakazu

doi:10.1007/s00200-020-00469-1

Cited by 1 publication

(4 citation statements)

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“…The second named author was not aware of the following simple expression when writing [8]. PROPOSITION 2.1.…”

Section: The Zeta Polynomial Of ϕ Nqmentioning

confidence: 99%

“…It is shown in [8,Theorem 2] that a homogeneous polynomial satisfying these three conditions exists if and only if…”

Section: Chebyshev Polynomials Of the First Kindmentioning

confidence: 99%

“…In [8], the second named author succeeded in giving a simple expression for Chinen's formal weight enumerators. To be precise, let q > 1 be a real number such that there exist integers n and j with…”

Section: Introductionmentioning

confidence: 99%

“…Note that q uniquely determines n and j, but for a fixed n ≥ 3 there are ϕ(n)/2 number of q, ϕ being Euler's totient function. The second named author showed in [8] that for such a q there exists a unique homogeneous polynomial ϕ n,q (x, y) with the following properties:…”

Section: Introductionmentioning

confidence: 99%

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On the Riemann Hypothesis for a Certain Family of Formal Weight Enumerators

KANEKO

Yamagishi²

2022

Kyushu J. Math.

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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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“…The second named author was not aware of the following simple expression when writing [8]. PROPOSITION 2.1.…”

Section: The Zeta Polynomial Of ϕ Nqmentioning

confidence: 99%

“…It is shown in [8,Theorem 2] that a homogeneous polynomial satisfying these three conditions exists if and only if…”

Section: Chebyshev Polynomials Of the First Kindmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations