Kernels of L-functions of cusp forms

被引：15
作者：
Diamantis, Nikolaos [2 ]
O'Sullivan, Cormac [1 ]
机构：
[1] CUNY Bronx Community Coll, Dept Math & Comp Sci, Bronx, NY 10453 USA
[2] Univ Nottingham, Dept Math, Nottingham NG7 2RD, England
来源：
MATHEMATISCHE ANNALEN | 2010年 / 346卷 / 04期
基金：
英国工程与自然科学研究理事会;
关键词：
EXPLICIT FORMULAS; HECKE OPERATORS; MODULAR-FORMS;
D O I：
10.1007/s00208-009-0419-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin's Periods Theorem. Cohen's representation of these kernels as series is also generalized.
引用
收藏
页码：897 / 929
页数：33
相关论文
共 27 条
[1]  
[Anonymous], 1973, Mat. Sb. (N.S.)
[2]   MODULAR-FORMS ON GAMMA-0(N) WITH RATIONAL PERIODS [J].
ANTONIADIS, JA .
MANUSCRIPTA MATHEMATICA, 1992, 74 (04) :359-384
[3]   Explicit formulas for Hecke operators on cusp forms, Dedekind symbols and period polynomials [J].
Fukuhara, Shinji .
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2007, 607 :163-216
[4]   Period polynomials and explicit formulas for Hecke operators on Γ0(2) [J].
Fukuhara, Shinji ;
Yang, Yifan .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2009, 146 :321-350
[5]  
Goldfeld D., 1999, ASIAN J MATH, V3, P729
[6]   HEEGNER POINTS AND DERIVATIVES OF L-SERIES [J].
GROSS, BH ;
ZAGIER, DB .
INVENTIONES MATHEMATICAE, 1986, 84 (02) :225-320
[7]  
IMAMOGLU O, 2009, ACTA ARITHM IN PRESS
[8]  
IWANIEC H, 1997, GRADUATE STUDIES MAT, V1
[9]  
Iwaniec H., 2002, Spectral Methods of Automorphic Forms, Vsecond
[10]   Convolution Dirichlet series and a Kronecker limit formula for second-order Eisenstein series [J].
Jorgenson, J ;
O'Sullivan, C .
NAGOYA MATHEMATICAL JOURNAL, 2005, 179 :47-102
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