Anticyclotomic p-adic L-function of Central Critical Rankin-Selberg L-value

作者：Brakocevic Miljan^*

来源：International Mathematics Research Notices, 2011, (21): 4967-5018.

DOI：10.1093/imrn/rnq275

Let M be an imaginary quadratic field, f a Hecke eigen-cusp form on GL(2)(Q)\GL(2)(A), and (pi) over cap (f) the unitary base-change to M of automorphic representation pi(f) associated to f. Take a unitary arithmetic Hecke character chi of M(x)\ M(A)(x) inducing the inverse of the central character of pi(f). The celebrated formula of Waldspurger relates the square of L(chi)(f) := integral(Mx\MAx) f(t)chi(t)d(x)t to the central critical value L(1/2, (pi) over cap (f) circle times chi). We construct a new p-adic L-function that interpolates L(chi)(f) over arithmetic chi's for a cusp form f in the spirit of the landmark result of Katz where he did that for the Eisenstein series.

• 出版日期2011