Title: Twisted Hecke L-values and period polynomials
Authors: Fukuhara, Shinji
Yang, Yifan
Department of Applied Mathematics
Keywords: Hecke operators;L-values;Modular forms (one variable);Period polynomials
Issue Date: 1-Apr-2010
Abstract: 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.
URI: http://dx.doi.org/10.1016/j.jnt.2009.09.009
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.09.009
Volume: 130
Issue: 4
Begin Page: 976
End Page: 999
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