Special values of L-functions modulo p

L 函数模 p 的特殊值

• 批准号: 228072-2009
• 负责人: Vatsal, Vinayak
• 金额: $ 3.06万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=524175
• 关键词: Special; values; functions; modulo

The current application proposes to study the Fourier coefficients of modular forms of half-integer weight by realizing them as theta constants arising from Mumford's theory of algebraic theta functions associated to polarized abelian varieties. In the case of interest, the abelian varieties are three-folds isogenous to the product of elliptic curves, and the polarization is deduced from a positive definite quadratic form in three variables.

当前的应用建议通过将半整数权值的模形式的傅里叶系数实现为由Mumford的与极化阿贝尔变相关的代数函数理论产生的θ常数来研究它们。在感兴趣的情况下，阿贝尔变量与椭圆曲线的乘积是三倍同质的，极化是由三个变量的正定二次形式推导出来的。