p-adic measures and square roots of special values of triple product L-functions
نویسنده
چکیده
Introduction Let p be a prime number. In this note, we combine the methods of Hida with the results of [HK1] to define a p-adic analytic function, the squares of whose special values are related to the values of triple product L-functions at their centers of symmetry. More precisely, let f , g, and h be classical normalized cuspidal Hecke eigenforms of level 1 and (even) weights k, l, and m, respectively, with k ≥ l ≥ m; assume k ≥ l+m. Let L(s, f, g, h) be the triple product L-function [G1, G2, PSR]; its center of symmetry is the point s = k+l+m−2 2 . Let < •, • >k be the normalized Petersson inner product for modular forms of weight k. Let Q{f, g, h} be the field generated over Q by the Fourier coefficients of f , g, and h. Using the integral representation for L(s, f, g, h) [op. cit], Kudla and one of the authors have shown that the quotient L( 2 , f, g, h) π2k < f, f >k ·C(k, l,m)
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