On the computation of the determinant of vector-valued Siegel modular forms

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2014-08-01 DOI:10.1112/S146115701400028X

S. Takemori

引用次数: 3

Abstract

Let A(Γ2) denote the ring of scalar valued Siegel modular forms of degree two, level 1 and even weights. In this paper, we prove the determinant of a basis of the module of vector valued Siegel modular forms ⊕ k≡ mod 2 Adetk ⊗Sym(j)(Γ2) over A (Γ2) is equal to a power of the cusp form of degree two and weight 35 up to a constant. Here j = 4, 6 and = 0, 1. The main result in this paper was conjectured by Ibukiyama [7].

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关于向量值西格尔模形式行列式的计算

设A(Γ2)表示二阶、一级、偶权的标量值Siegel模形式环。在本文中，我们证明了向量值的Siegel模形式的模的基的行列式⊕k≡mod2 adek⊗Sym(j)(Γ2) / a (Γ2)等于2次和权值为35的尖形的幂直至一个常数。这里j =(4,6)和= (0,1)本文的主要结果是由Ibukiyama b[7]推测出来的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.