Anticyclotomic p-adic L-function of central critical Rankin-Selberg L-value

Details Anticyclotomic p-adic L-function of central critical Rankin-Selberg L-value Anticyclotomic p-adic L-function of central critical Rankin-Selberg L-value

2010-07-29

arxiv.org/abs/1007.5124v2

Mathematics

Number Theory

30 pages. Final version, to appear in IMRN. The proof of Lemma 8.2 revised, referee's suggestions incorporated, results unchan

Scientific paper

Let M be an imaginary quadratic field, f a Hecke eigenform on GL2(Q) and \pi the unitary base-change to M of the automorphic representation associated to f. Take a unitary arithmetic Hecke character \chi of M inducing the inverse of the central character of f. The celebrated formula of Waldspurger relates the square of an integral L(f) of f and \chi over the idele class group of M to the central critical value L(1/2,{\pi}\otimes{\chi}). In this paper, we present a construction of a new p-adic L-function that interpolates L(f) over arithmetic characters for a cusp form f in the spirit of the landmark result of Katz where he did that for Eisenstein series.

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