关于一类形式权重枚举数的黎曼假设

Pub Date : 2022-01-01 DOI:10.2206/kyushujm.76.441

Naoya Kaneko, Masakazu Yamagishi

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摘要

．形式权重枚举数是两个变量的齐次多项式，其行为类似于自对偶线性码的汉明权重枚举数，只是其系数不一定是非负整数。Chinen发现了几个正式权重枚举数族，并研究了黎曼假设类比对它们的有效性。本文计算了Chinen形式权重枚举数的zeta多项式，并给出了Riemann假设类比有效性的一个简单判据。实数q > 0, q (cid:54)= 1。此外，如果A σ (x, y) = ε A (x, y)成立

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ON THE RIEMANN HYPOTHESIS FOR A CERTAIN FAMILY OF FORMAL WEIGHT ENUMERATORS

. 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. real number q > 0 , q (cid:54)= 1. Moreover, if A σ ( x , y ) = ε A ( x , y ) holds for the

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