Research on special values of the standard L-functions of Siegel modular forms and related fields
Research on special values of the standard L-functions of Siegel modular forms and related fields
批准号:
15540003
负责人:
KATSURADA Hidenori
金额:
$2.37万
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
项目状态:
已结题
起止时间:
2003 至 2004
中文摘要
(1)考虑了标准Zeta函数的特殊值与任意次Siegel尖点形式的同余之间的关系。特别地,我提出了关于尖顶Hecke本征形关于SL(2,Z)的Saito-Kurokawa升力与其L函数的特定值的同余的猜想,并在一定条件下证明了这一猜想。此外,我们还给出了一些数字证据来支持我们的猜想。我在2004年10月在白场举行的研讨会上和2005年3月在Karatsu举行的会议上就这些问题进行了演讲。(2)设M和N是无平方正整数,φ和χ分别是Dirichlet特征标mod M和N。对于Neben型φ的尖锥Hecke本征形式f,我给出了f被χ扭成的标准Zeta函数的特例的显式公式。我给出了这些值的数值例子,并检验了Block-Kato猜想得到的一些结果。(3)证明了二次Nebent型自由平方能级Eisenstein级数的空间是由亏格theta级数与R.Schulze-Pillot共同跨越的。利用这一结果,我证明了二次Nebent型自由平方能级的尖点形式的空间是由S.Boecherer和R.Schulze-Pillot共同建立的theta级数所跨越的。他们在2004年9月在立交大学举行的研讨会上就这些问题进行了讨论。(4)我与T.Ibukiyama共同给出了真正解析Eisenstein级数的Koecher-Maass级数的显式形式。2004年9月,我在日本立交大学举行的研讨会上就这一问题发表了演讲。
英文摘要
(1)I considered the relation between special values of the standard zeta functions and the congruence a Siegel cusp form of arbitrary degree. In particular, I proposed a conjecture concerning the congruence of the Saito-Kurokawa lift of a cuspidal Hecke eigenform with respect to SL(2,Z) and the special value of its L-function, and proved it under certain condition. Furthermore we gave some numerical evidence for our conjecture. I gave talks on these topics at the workshop held at Hakuba on October 2004, and at the conference held at Karatsu on March 2005.(2)Let M and N be square free positive integers, and φ and χ be Dirichlet characters mod M and N, respectively. For a cuspidal Hecke eigenform f of neben type φ I gave an explicit formula for the special values of the standard zeta function of f twisted by χ. I gave numerical examples for these values and checked some results derived from the Block-Kato conjecture.(3)I proved that the space of Eisenstein series of square free level of quadratic nebentype is spanned by the genus theta series jointly with R. Schulze-Pillot. By using this result, I proved that the space of cusp forms of square free level of quadratic nebentype is spanned by the theta series jointly with S.Boecherer and R.Schulze-Pillot. They gave talks on these topics at the symposium held at Rikkyo University on September 2004.(4)I gave an explicit form of the Koecher-Maass series for the real analytic Eisenstein series jointly with T.Ibukiyama. I gave a talk on this topic at the symposium held at Rikkyo University on September 2004.
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Hall's relations in finite groups.
有限群中的霍尔关系。
DOI:
--
发表时间:
2004
期刊:
Journal of Algebra 371
影响因子:
--
作者:
[TAKAGAHARA, Yugen]
通讯作者:
Yugen
An explicit formula for the Koecher-Maass Dirichlet series for the Ikeda lifting
池田提升的 Koecher-Maass Dirichlet 级数的显式公式
DOI:
--
发表时间:
2004
期刊:
Abhand.Math.Sem.der Univ.Hamburg 74
影响因子:
--
作者:
[T.Ibukiyama, H.Katsurada]
通讯作者:
H.Katsurada
T.Ibukiyama: "An explicit form of the Koecher-Maass Dirichlet series for klingen's Eisenstein series"J.Number Theory. 71. 223-256 (2003)
T.Ibukiyama:“克林根爱森斯坦级数的 Koecher-Maass Dirichlet 级数的显式形式”J.数论。
DOI:
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发表时间:
期刊:
影响因子:
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作者:
[]
通讯作者:
An explicit form of the Koecher-Maass Dirichlet series for Klingen's Eisenstein series
克林根爱森斯坦级数的 Koecher-Maass Dirichlet 级数的显式形式
DOI:
--
发表时间:
2003
期刊:
J.Number Theory 71
影响因子:
--
作者:
[Masaaki Amou, Masanori Katsurada, T.Ibukiyama]
通讯作者:
T.Ibukiyama
H.Katsurada: "Pullback formula of Eisenstein series and its applications"第2回保型形式周辺分野スプリングコンファレンス報告集. 167-204 (2004)
H. Katsurada:“爱森斯坦级数的回拉公式及其应用”第二届自守形式春季会议报告 167-204 (2004)。
DOI:
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发表时间:
期刊:
影响因子:
--
作者:
[]
通讯作者:
共 21 条
Periods, congruence and special values of L functions for modular forms
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批准号:16H03919
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项目类别:Grant-in-Aid for Scientific Research (B)
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资助金额:$8.49万
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财政年份:2016
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负责人:KATSURADA Hidenori
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依托单位:
Perrods and cogruences of modular forms
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批准号:24540005
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$3.33万
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财政年份:2012
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负责人:KATSURADA Hidenori
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依托单位:
Periods and congruence of modular forms, and Selmer group
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批准号:21540004
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.91万
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财政年份:2009
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负责人:KATSURADA Hidenori
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依托单位:
Research on special values on L-functions of automorphic forms
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批准号:17540003
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.43万
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财政年份:2005
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负责人:KATSURADA Hidenori
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依托单位:
Investigation of Koecher-Maass series for various liftings of Siegel modular forms
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批准号:13640003
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.62万
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财政年份:2001
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负责人:KATSURADA Hidenori
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依托单位:
Investigation of Dirichlet series for Siegel modular forms
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批准号:11640002
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.43万
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财政年份:1999
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负责人:KATSURADA Hidenori
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依托单位:
Investigation of Eisenstein series on bounded symmeric domain
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批准号:09640002
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.24万
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财政年份:1997
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负责人:KATSURADA Hidenori
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依托单位:
Local densities of quadratic forms and related problems
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批准号:06640003
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项目类别:Grant-in-Aid for General Scientific Research (C)
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资助金额:$1.41万
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财政年份:1994
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负责人:KATSURADA Hidenori
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依托单位: