Anticyclotomic p-adic L-function of central critical Rankin-Selberg L-value
arXiv:1007.5124 · doi:10.1093/imrn/rnq275
Abstract
Let M be an imaginary quadratic field, f a Hecke eigenform on GL2(Q) and πthe unitary base-change to M of the automorphic representation associated to f. Take a unitary arithmetic Hecke character χof 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 χover the idele class group of M to the central critical value L(1/2,π\otimesχ). 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.
arXiv comment30 pages. Final version, to appear in IMRN. The proof of Lemma 8.2 revised, referee's suggestions incorporated, results unchanged, minor typos corrected