论文信息 - A Riemann hypothesis analogue for invariant rings

A Riemann hypothesis analogue for invariant rings

A Riemann hypothesis analogue for coding theory was introduced by I.M. Duursma [A Riemann hypothesis analogue for self-dual codes, in: A. Barg, S. Litsyn (Eds.), Codes and Association Schemes (Piscataway, NJ, 1999), American Mathematical Society, Providence, RI, 2001, pp. 115-124]. In this paper, we extend zeta polynomials for linear codes to ones for invariant rings, and we investigate whether a Riemann hypothesis analogue holds for some concrete invariant rings. Also we shall show that there is some subring of an invariant ring such that the subring is not an invariant ring but extremal polynomials all satisfy the Riemann hypothesis analogue.

Tetsuo Harada | Makoto Tagami | M. Tagami | Tetsuo Harada

[1] Iwan M. Duursma. From weight enumerators to zeta functions , 2001, Discret. Appl. Math..

[2] Shengyuan Zhang. On the nonexsitence of extremal self-dual codes , 1999 .

[3] Iwan M. Duursma. Extremal weight enumerators and ultraspherical polynomials , 2003, Discret. Math..

[4] Edmund Taylor Whittaker,et al. A Course of Modern Analysis , 2021 .

[5] Iwan M. Duursma. A Riemann hypothesis analogue for self-dual codes , 1999, Codes and Association Schemes.

[6] Iwan M. Duursma,et al. Weight distributions of geometric Goppa codes , 1999 .

[7] W. André. Courbes algébriques et variétés abéliennes , 1971 .

[8] G. C. Shephard,et al. Finite Unitary Reflection Groups , 1954, Canadian Journal of Mathematics.

[9] F. MacWilliams,et al. The Theory of Error-Correcting Codes , 1977 .