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arXiv · 1007.5124

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

Miljan Brakočević
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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.

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Miljan Brakočević. 2010-11-25. Anticyclotomic p-adic L-function of central critical Rankin-Selberg L-value. https://doi.org/10.1093/imrn%2Frnq275

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