Divisibility of anticyclotomic L-functions and theta functions with complex multiplication
نویسندگان
چکیده
منابع مشابه
Special Values of Anticyclotomic L-functions
The purpose of the paper is to extend and refine earlier results of the author on nonvanishing of the L-functions associated to modular forms in the anticyclotomic tower of conductor p over an imaginary quadratic field. While the author’s previous work proved that such L-functions are generically nonzero at the center of the critical strip, provided that the sign in the functional equation is +...
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We give a new construction of a p-adic L-function L(f,Ξ), for f a holomorphic newform and Ξ an anticyclotomic family of Hecke characters of Q( √ −d). The construction uses Ichino’s triple product formula to express the central values of L(f, ξ, s) in terms of Petersson inner products, and then uses results of Hida to interpolate them. The resulting construction is well-suited for studying what ...
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p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication
The study of non-abelian fundamental groups renders it plausible that the principle of Birch and Swinnerton-Dyer, whereby non-vanishing of L-values, in some appropriate sense, accounts for the finiteness of integral points, can eventually be extended to hyperbolic curves. Here we will discuss the very simple case of a genus 1 hyperbolic curve X/Q obtained by removing the origin from an elliptic...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2006
ISSN: 0003-486X
DOI: 10.4007/annals.2006.163.767