Twisted Hecke L-values and period polynomials

JOURNAL OF NUMBER THEORY

卷:130

Article

Fukuhara, Shinji¹  Yang, Yifan² 

[1] Tsuda Coll, Dept Math, Kodaira, Tokyo 1878577, Japan

[2] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 300, Taiwan

关键词: Hecke operators;    L-values;    Modular forms (one variable);    Period polynomials;   

DOI  :  10.1016/j.jnt.2009.09.009

来源: Elsevier

【 摘 要 】

Let f(1),..., f(d) be an orthogonal basis for the space of cusp forms of even weight 2k on Gamma(0)(N). Let (f(i), s) and L(f(i), chi, s) denote the L-function of f(i) and its twist by a Dirichlet character chi, respectively. In this note, we obtain a trace formula for the values L(f(i), chi, m)<(L(f(i), n))over bar> at integers m and n with 0 < m, n < 2k and proper parity. In the case N = 1 or N = 2, the formula gives us a convenient way to evaluate precisely the value of the ratio L(f, chi, m)/L(f, n) for a Hecke eigenform f. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free