Local densities of quadratic forms and related problems

二次型局部密度及相关问题

• 批准号: 06640003
• 负责人: KATSURADA Hidenori
• 金额: $ 1.41万
• 依托单位: Muroran Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06640003/
• 关键词: Local densities; Siegel-Eisenstein series; Maass zeta function; ジーゲル アイゼンシュタイン級数; マ-ス ゼータ関数; ジーゲル-アイゼンシュタイン級数

In this research, we found a recursion formula for local densitires, which is useful to give an explicit formula for local desities. Further applying this to Sigel-Eisenstein series, we gave several important results about the Fourier coefficients of Siegel-Eisenstein series.First, we gave a precise information about the denominator of a power series of one variables defined by Y.Kitaoka.Secondly, we gave an explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3.Thirdly, we gave an explicit formula for Koecher-Maass Dirichlet series associated with Siegel-Eisenstein series. This is a joint work with T.Ibukiyama.Finally we gave a precise information about the denominaotor and numerator of a power series of several variables attached to local densities of quadratic forms.

在这项研究中，我们发现了局部密度的递归公式，这对于给出局部剂量的明确公式很有用。 Further applying this to Sigel-Eisenstein series, we gave several important results about the Fourier coefficients of Siegel-Eisenstein series.First, we gave a precise information about the denominator of a power series of one variables defined by Y.Kitaoka.Secondly, we gave an explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3.Thirdly,我们给出了与Siegel-Eisenstein系列相关的Koecher-Maass Dirichlet系列的明确公式。这是与t.ibukiyama的联合作品。在本文中，我们提供了有关二次形式局部密度的几个变量的幂序列的幂来的精确信息。

项目成果

Katsuroda,H: "A certain formal power series of several variables attached to local densities of quadratic forms I" J.Number Theory. 51. 169-209 (1995)

Katsuroda，H：“与二次形式 I 的局部密度相关的几个变量的某个形式幂级数”J.数论。

桂田英典: "A recursion formula for local demsities" 日本数学会代数分科会講演アプストラクト. 13-14 (1994)

Hidenori Katsurada：“A recursion Formula for local demsities” 日本数学会代数小组委员会演讲摘要 13-14 (1994)。

H.Katsurada: "A certain formal power series of several variables attached to local densities of quadratic forms I" J.Number Theory. 51. 169-209 (1995)

H.Katsurada：“与二次形式 I 的局部密度相关的几个变量的某种形式幂级数”J.Number Theory。

Katsurada,H: "Calculation of the Fourier coefficients of Siegel Eisenstein series" “代数と計算機"シンポジウム報告集. (発表予定). (1996)

Katsurada, H：“Siegel Eisenstein 级数的傅里叶系数的计算”“代数和计算器”研讨会报告（待提交）。

Katsurada, H: "On power series attache to local denisities" Proc. Japan Acad.71. 187-188 (1995)

Katsurada, H：“关于当地否认的权力系列专员”Proc。