Central values of L-functions over CM fields
نویسندگان
چکیده
منابع مشابه
Central Values of Hecke L-functions of Cm Number Fields
0. Introduction. It is well known that the zeta function of CM (complex multiplication) abelian varieties can be given in terms of L-functions of associated Hecke characters. In this paper, we prove a formula expressing the central special value of the L-function of certain Hecke characters in terms of theta functions. The formula easily implies that the central value is nonnegative and yields ...
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Let κ′, κ ≥ 3 be two odd integers. Let f (resp. g) be a normalized holomorphic modular form of weight 2κ (resp. κ′ + 1) and level one on the upper half plane h. Assume that they are Hecke eigenforms. Let L(s, Sym g×f) be the completed degree six L-function and we normalize so that s = 1 2 is the center of symmetry. Let 〈−,−〉 be the Petersson inner product, defined using the usual measure on h s...
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How fast can we compute the value of an L-function at the center of the critical strip? We will divide this question into two separate questions while also making it more precise. Fix an elliptic curve E defined over Q and let L(E, s) be its L-series. For each fundamental discriminant D let L(E,D, s) be the L-series of the twist ED of E by the corresponding quadratic character; note that L(E, 1...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.05.010