Studies on unified theory of zeta functions

Zeta函数统一理论研究

• 批准号: 10640009
• 负责人: KUROKAWA Nobushige
• 金额: $ 0.77万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640009/
• 关键词: zeta function; category; spectrum; unified theory; arithmetical algebraic geometry; 代数多様体; 力学系; 保型表現

We studied the unified theory of zeta functions.Kurokawa studied categorical aspects. Saito studied arithmetical aspects. Morita studied analytical aspects. Mizumoto studied algebraic aspects. We sketch their studies.Kurokawa published a study on the spectra of Laplace operators of categories containing the semipositivity and the asymptotic spectral distribution. The Laplace operator of a category is a symmetrical matrix consisting of the number of arrows between two objects and its properties are interesting from many view points. Kurokawa studied also Selberg zeta functions, and obtained an explicit formula for the multiplicities of specta. A general theory of zeta functions of algebraic systems. Mizumoto studied orders of zeros of zeta functions at the center of the functional equations, and obtained the unboundedness. Morita made the analytic continuation of the zeta function associated to a two dimensional billiard. Saito studied arithmetical algebraic geometry around algebraic cycles.These studies present a frame for the unified theory of zeta functions.

我们研究了Zeta函数的统一理论。川川研究了分类方面。 Saito研究了算术方面。莫里塔研究了分析方面。 Mizumoto研究了代数方面。我们绘制了他们的研究。Kurokawa发表了一项关于包含半阳性和渐近光谱分布的类别拉普拉斯操作员光谱的研究。类别的拉普拉斯运算符是一个对称矩阵，该矩阵由两个对象之间的箭头数组成，从许多角度来看，它都很有趣。黑川还研究了Selberg Zeta功能，并获得了Specta多重性的明确公式。代数系统的Zeta功能的一般理论。 Mizumoto研究了功能方程中心的Zeta函数零的顺序，并获得了无界度。莫里塔（Morita）进行了与二维台球相关的zeta功能的分析延续。 Saito研究了围绕代数循环的算术代数几何形状。这些研究提出了Zeta函数统一理论的框架。

项目成果

黒川信重: "リーマン予想"数学セミナー. 38. 60-64 (1999)

黑川信成：“黎曼猜想”数学研讨会。38. 60-64 (1999)

N. Kurokawa, M. Wakayama: "A formula for the multiplicity of Principal series"Forum Mathematicum. (印刷中).

N. Kurokawa，M. Wakayama：“主级数重数的公式”数学论坛（正在出版）。

黒川信重: "リーマン予想"数学セミナー. 38・ 11. 60-64 (1999)

黑川信重：“黎曼猜想”数学研讨会。38・11.60-64（1999）

S. Mizumoto: "Certain L-functions at s=1/2"Acta arithmetica. vol. 88. 51-66 (1999)

S. Mizumoto：“s=1/2 处的某些 L 函数”Acta 算术。

水本 信一郎: "Certain L-functions at S=1/2" Acta Arithmetica. (印刷中). (1998)

Shinichiro Mizumoto：“S=1/2 时的某些 L 函数”Acta Arithmetica（正在出版）。