Stadies on Andytic Priepeitied of autoinoiptic L-functions

安迪克增强自力L-功能的研究

• 批准号: 16340002
• 负责人: MATSUMOTO Koji
• 金额: $ 11.21万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340002/
• 关键词: automcrphic L-function; automacrphic form; automcrphic L-fiuiction; Ikeda lifting; mean-valat fheoreul; multiple zeta-fanction; multiple L-function; 平均値定理; Wittenゼータ関数; ルート系; 半単純Lie環; 関数関係式; Weyl群; 関数等式; Siegelモジュラー形式; 二乗平均値定理; スタンダードL関数 /

First, we have developed the theory of modular relations and have given a unified treatment of functional equations, approximate functional equations and asymptotic expansions in view of modular relations. From this viewpoint, we gave a modular-theoretic proof of asymptotic expansion formulas of Katsurada and Matsumoto on Dirichlet L-functions and Hurwitz zeta-functions. Secondly, on Ikeda liftings of Siegel modular forms, we have shown-a part of Kohnen's conjecture on the image space of Ikeda liftings. We have proved rather sharp asymptotic formula for the mean square of standard L-functions attached to modular forms which are Ikeda lifts. In particular, applying a large value lemma, we almost determined the true order of the mean square in some cases. As for the theory of multiple zeta-functions, we have developed the study of double shuffle relations of multiple zeta values, and have clarified their arithmetic structure. Also we discovered that the functional relations among multiple zeta-functions can be explained by the symmetry of Weyl groups of underlying Lie algebras. Moreover we have found that the recursive structure of the family of multiple zeta-functions can be described in terms of Dynkin diagrams.

首先，我们发展了模块化关系的理论，并以模块化关系给出了功能方程，近似功能方程和渐近扩展的统一处理。从这个角度来看，我们在Dirichlet L功能和Hurwitz Zeta-Inctions上给出了Katsurada和Matsumoto的渐近扩张公式的模块化理论证明。其次，在Siegel模块化形式的Ikeda升降机上，我们在Ikeda升降机的图像空间上显示了Kohnen的猜想的一部分。我们证明，对于iKeda升降机的模块化形式，标准L功能的均匀平方是相当尖锐的渐近公式。特别是，在某些情况下，我们几乎确定了均方根的真实顺序。至于多个Zeta功能的理论，我们已经开发了多个Zeta值的双层杂交关系的研究，并阐明了它们的算术结构。我们还发现，多个Zeta功能之间的功能关系可以通过基础谎言代数的Weyl群的对称性来解释。此外，我们发现可以用Dynkin图来描述多个Zeta功能的家族的递归结构。

项目成果

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

Canvolutions of the von Mangoldt function and related Dirichlet series

von Mangoldt 函数和相关 Dirichlet 级数的卷积

• 发表时间: 2007
• 期刊: in "Number Theory", Series on Number Theory and its Appl. 2
• 作者: S. Egami;K. Matsumoto
• 通讯作者: K. Matsumoto

On witten multiple zeta-fuuctions associated with semisimple Lie algebras I

论与半单李代数相关的多重 zeta 函数 I

• 发表时间: 2006
• 期刊: Ann. Inst. Fourier 56
• 作者: K.Matsumoto;H.Tsumura
• 通讯作者: H.Tsumura

On the discrete mean square of Dirichlet L-functions at 1

关于 1 处 Dirichlet L 函数的离散均方

• 发表时间: 2004
• 期刊: Math.Z. 248
• 作者: S.Kanemitsu;Y.Tanigawa;M.Yoshimoto;W.Zhang
• 通讯作者: W.Zhang

Liftings and mean value theorems for automorphic L-functions

自守 L 函数的提升和中值定理

• 发表时间: 2005
• 期刊: Proc.London Math.Soc. (3)90
• 作者: Kato;Kazuya; Saito;Takeshi;K.Matsumoto
• 通讯作者: K.Matsumoto