Research On The Bernoulli Numbers Attached Formal Group

伯努利数附属形式群的研究

• 批准号: 15540019
• 负责人: SATOH Junya
• 金额: $ 2.3万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540019/
• 关键词: formal group; number theory; zeta function; Bernoulli numbers; Kronecker density; power residue; reciprocity law; code theory; distribution relation

(1) We extend a well-known distribution relation for ordinary Bernoulli polynomials to that of Bernoulli polynomials attached to formal group.(2) A conflict-avoiding code (CAC) C of length n with weight k is a family of binary sequences of length n and weight k satisfying P_0 t_<njl> x_<it>x_<j ; t+s>・, for any distinct codewords X_i= (X_<iO>, X_<il>;:::; X_<i ; nj1>) and X_j = (x_<jo>, x_<jl>;:::; X_<j ; nj1>) in C and for any integer s, where the subscripts are taken modulo n. A CAC with maximal code size for given n and k is said to be optimal. A CAC has been studied for sending messages correctly through a multiple-access channel. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, the case, = 1 is treated, and various direct and recursive constructions of optimal CACs for weight k = 4 and 5 are obtained by providing constructions of CACs for general weight k. In particular, the maximum code size of CACs satisfying certain sufficient conditions is determined through number theoretical and combinatorial approaches.

(1)本文将一个著名的普通伯努利多项式的分布关系推广到形式群上的伯努利多项式的分布关系。(2)长度为n、重量为k的避免冲突码（CAC）C是一类长度为n、重量为k的二元序列，对于C中<njl><it>任意不同的码字X_i=（X_<iO>，X_<il>;：：; X_&lt;i ; nj 1&gt;）和X_j =（x_<jo>，x_<jl>;：：; X_&lt;j ; nj 1&gt;）以及任意整数s，其下标取模n，满足P_0 t_ x_ x_&lt;j ; t+s&gt;·。对于给定的n和k，具有最大代码大小的CAC被称为最优的。一个CAC已被研究通过多路访问信道正确发送消息。最佳CAC的使用使得尽可能多的异步用户能够高效可靠地传输信息。本文讨论了k = 1的情形，通过给出一般权k的CAC的构造，得到了权k = 4和5的各种最优CAC的直接和递归构造。特别地，通过数论和组合方法确定了满足一定充分条件的CAC的最大码长。

项目成果

Bounds and Constructions for Optimal Constant Weight Conflict-Avoiding Codes

最佳恒重冲突避免代码的界限和构造

• 发表时间: 2007
• 期刊: Procceding of 2007 IEEE International Symposium on Information Theory
• 作者: K.Momihara;M.Muller;J.Satoh;M.Jimbo
• 通讯作者: M.Jimbo

Distribution relation for Bernoulli polynomials attached to formal group

附属于形式群的伯努利多项式的分布关系

• 发表时间: 2003
• 期刊: Preprint Ser.in Math. Sci.,Nagoya University 2003-1
• 作者: Yasuo Yoshinobu;M. Kada;K. Tomoyasu;Junya Satoh
• 通讯作者: Junya Satoh

How many miles to βω? - Approximating βω by metric-dependent compactifications

βω 有多少英里？ - 通过与度量相关的压缩来近似 βω

• 发表时间: 2004
• 期刊: Topology and its Applications 145
• 作者: Yasuo Yoshinobu;M. Kada;K. Tomoyasu
• 通讯作者: K. Tomoyasu

Stationary preserving ideals over P k λ

P k λ 上的稳态保持理想

• 发表时间: 2003
• 期刊: J. the Math. Soc. Japan 55-3
• 作者: Yasuo Yoshinobu;M. Kada;K. Tomoyasu;Junya Satoh;Yo Matsubara;Junya Satoh;Yo Matsubara
• 通讯作者: Yo Matsubara

On the mean square of standard L-functions attached to Ikeda lifts

池田电梯附带的标准 L 函数的均方

• 发表时间: 2006
• 期刊: Math. Z. 253
• 作者: Kohji Matsumoto;A. Sankaranarayanan
• 通讯作者: A. Sankaranarayanan