Twisted Hecke L-values and period polynomials
Journal
Journal of Number Theory
Journal Volume
130
Journal Issue
4
Pages
976-999
Date Issued
2010
Author(s)
Fukuhara, S.
Abstract
Let f1, ..., fd be an orthogonal basis for the space of cusp forms of even weight 2k on Γ0 (N). Let L (fi, s) and L (fi, χ, s) denote the L-function of fi and its twist by a Dirichlet character χ, respectively. In this note, we obtain a "trace formula" for the values L (fi, χ, m) over(L (fi, n), -) at integers m and n with 0 < m, n < 2 k 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, χ, m) / L (f, n) for a Hecke eigenform f. © 2009 Elsevier Inc. All rights reserved.
Type
journal article