Mean square values of Hecke L-series formed with r-th order characters

• 成果类型: Article
• 署名作者: Diaconu, A
• 署名单位: Columbia University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0363-6
• 发表日期: 2004
• 页码: 635-684
• 关键词: metaplectic eisenstein series; automorphic l-functions; nonvanishing theorems; fourier coefficients; modular-forms; dirichlet series; function-fields; theta-series; derivatives; twists

摘要

Let L be a number field containing the r-th roots of unity. Starting with the Rankin-Selberg convolution of a metaplectic Eisenstein series on the r-fold cover of GL(2) with itself, we construct a Dirichlet series defined over L whose coefficients involve the r-th order twists of a fixed Hecke L-function. We then observe that a group of functional equations can be naturally associated with this construction. Combining this with the convexity theorem for holomorphic functions of several complex variables, we show that this object, as a function of two complex variables, admits meromorphic continuation to C-2. As an application, we obtain asymptotic formulae for mean square values of the r-th order twists of an arbitrary Hecke L-function defined over L.