Integral mean values of modular L-functions
نویسندگان
چکیده
منابع مشابه
Congruences for Fourier Coefficients of Half-integral Weight Modular Forms and Special Values of L−functions
Congruences for Fourier coefficients of integer weight modular forms have been the focal point of a number of investigations. In this note we shall exhibit congruences for Fourier coefficients of a slightly different type. Let f(z) = P∞ n=0 a(n)q n be a holomorphic half integer weight modular form with integer coefficients. If ` is prime, then we shall be interested in congruences of the form
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(for the precise definition of ω, see Section 2.) The analytic properties of this Dirichlet series were investigated by Shimura [12] (see also Mizuno, [10].) Furthermore the algebraicity of the values of this Dirichlet serries evaluated at halfintegers was deeply investigated by Shimura [12]. However, as far as we know, there is no result about the algebraicity of its special values at integers...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2005
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.10.007