Arithmetic study of Fourier coefficients of modular forms of half integral weight and the special values of zeta functions

半积分权模形式傅里叶系数及zeta函数特殊值的算术研究

• 批准号: 14540002
• 负责人: KOJIMA Hisashi
• 金额: $ 2.24万
• 依托单位: IWATE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540002/
• 关键词: modular forms of half integral weight; zeta function; Jacobi form; modular forms; Maass wave form

W.Kohnen reformulated the Ikeda lifting as a linear mapping and he formulated a Maass space of Siegel modular forms of degree 2n. Moreover, he purposed a conjecture that the image of Ikeda lifting is equal to the Maass space of degree 2n. In a joint work with W.Kohnen, we proved that this conjecture is ture in the case where 4|n and 4|n-1.

W.Kohnen 将 Ikeda 提升重新表述为线性映射，并制定了 2n 次 Siegel 模形式的 Maass 空间。而且，他还提出了池田升起的图像等于2n次马斯空间的猜想。在与 W.Kohnen 的合作中，我们证明了这个猜想在 4|n 和 4|n-1 的情况下是正确的。

项目成果

Hisashi Kojima: "On the Fourier coefficients of Hilbert-Maass wave forms of half integral weight over arbitrary algebraic number fields"J.Number theory. 107(to appear). 25-62 (2004)

Hisashi Kojima：“任意代数数域上半积分权重的希尔伯特-马斯波形的傅里叶系数”J.数论。

Genichi Oshikiri: "A divergence-like characterization of admissible functions of digraphs"Tohoku Math.J.. (submitted)(to appear).

Genichi Oshikiri：“有向图的可接受函数的类散度表征”Tohoku Math.J..（已提交）（待出现）。

Hisashi Kojima: "Pemark on the dimension of Kohnen's space of Holfintigral weight with square free livel"Proceedings of the Japan Academy, Ser. A. Vol.78No.2. 18-21 (2002)

小岛恒：“Pemark on Kohnens space of Holfintigral Weight with square free livel”日本学院院刊，Ser.

Hisashi Kojima: "Remark on the dimension of Kohnen's spaces of half integral weight with square free level"Proc.Japan Acad.. 78. 18-21 (2002)

小岛恒：“关于具有平方自由水平的半积分权的 Kohnen 空间的维数”Proc.Japan Acad.. 78. 18-21 (2002)

J.Brudern, K.Kawada, T.D.Wooley: "Additive representation in thin sequenses, V : mixed problems of Waring's type"Math.Scand.. 92. 181-209 (2003)

J.Brudern、K.Kawada、T.D.Wooley：“薄序列中的加法表示，V：Waring 类型的混合问题”Math.Scand.. 92. 181-209 (2003)