ジョルダン代数のゼ-ヌ関数と保型形式の次元

Jordan 代数的 Zene 函数和自守形式的维数

• 批准号: 07210252
• 负责人: 伊吹山 知義
• 金额: $ 0.51万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-07210252/
• 关键词: ジョルダン代数; 保型形式; 次元公式; 跡公式; アイゼンショタイン級数

1.本年度は、対称行列のなすJordan algebra内のconeのゼータ関数として、重さk(整数)の次数nのSiegel Eisenstein級数 E^n_k(Z)に付随するKoecher Maassのディリクレ級数L(s,E^n_k(Z))(E^n_k(Z)のMellin変換で得られるゼータ関数)を取り上げた。今年度のこの研究における主定理として、任意のnに対して、L(s,E_n^κの完全に具体的な公式を得た。このゼータ関数の具体型はn=1は古典的によく知られている。また、n=2はフーリエ係数のMaassによる公式から、Boechererが導いている。しかし、一般の公式は予想等もこめても、全くなにも知られていなかった。結論は、多くの専門家の思いこみに反して、いたって単純な形に記述される。すなわち、nが奇数ならリーマンゼータ関数の平行移動の積の2つの線形結合になり、またnが偶数なら、重さ半整数の2つの1変数Eisenstein級数のMellin変換のconvolution productとリーマンゼータの平行移動の積、およびリーマンゼータの平行移動の積の2つのディリクレ級数の和になる。(以上桂田英典氏との共同研究による。)以上の結果の要約は数理解析研究所講究録に掲載予定。また、英文論文は準備中。保型形式の次元公式のために使用する、概均質ベクトル空間のゼータ関数と跡公式の核関数の間の関数等式、および次元公式の寄与への関係についての研究者の成果を数理解析研究所講究録に公表した。

1. In this year, the Siegel Eisenstein series E^n_k(Z) of the number n of cone in Jordan algebra (E^n_k (Z))(E ^n_k (Z) of Mellin transformation) is selected. In this paper, the main theorem, arbitrary n pairs, L(s,E_n^κ) and completely concrete formulas are obtained. The number of specific types of n=1 and classical n=1 are known as n=1 and n = 1 respectively. , n=2 The general formula is to wait for the answer, and the whole thing is to know it. The conclusion is that there are many ways to describe the relationship between the two countries. The linear combination of 2 sets of products of parallel movements of odd numbers, n sets of even numbers, n sets of weights of 2 sets of 1 sets of Eisenstein series of Mellin transformations of convolution products of parallel movements, n sets of products of parallel movements, n sets of even numbers, n sets of weights of 2 sets of linear combinations of products of parallel movements, n sets of even numbers, n sets of weights of 2 sets of linear combinations of products of parallel movements, n sets of even numbers, n sets of even numbers, n sets of weights of 1 sets of Eisenstein series of Mellin transformations of convolution products of parallel movements, n sets of even numbers, n sets of even numbers, n sets of products of parallel movements, n sets of 2 sets of linear combinations of products of 2 sets of product of parallel movements, n sets of even numbers, n sets of even numbers, n sets of weights of 1 sets of weights of 1 sets of 1 sets of Eisenstein series of Mellin transformations of convolution products of 2 sets of products of parallel movements, n sets of 1 sets of even numbers, n sets of even numbers of 1 (The above joint research by Katsuda Hidenori.) The above results are presented in the journal of the Institute of Mathematical Analysis. English papers are being prepared. The results of the researchers in the field of mathematical analysis and research on the relationship between the dimensional formula of the type preserving form and the relationship between the dimensional formula and the trace formula are recorded in the table.

项目成果

伊吹山 知義: "An explict for uia for qctu ctionsa vedo spece" 京都大学数理解析研究所講究録. 924. 88-101 (1995)

Tomoyoshi Ibukiyama：“An Explict for uia for qctu ctionsa vedo spece”京都大学数学分析研究所 Kokyuroku。 924. 88-101 (1995)

T.Ibukiyama: "On qeta functions anociated to Symmetvic matricas I" Amer,J.Math.117. 1097-1155 (1995)

T.Ibukiyama：“论与对称矩阵 I 相关的 qeta 函数”Amer，J.Math.117。

伊吹山 知義: "On clim ensis of antonaplic from and qeto simctions of prehonoochors vedr space" 京都大学数理解析研究所講究録. 924. 127-133 (1995)

Tomoyoshi Ibukiyama：“On clim ensis of antonaplic from and qeto simctions of prehonochors vedr space” 京都大学数学科学研究所 Kokyuroku. 924. 127-133 (1995)