Anticyclotomic p-adic L-function of central critical Rankin-Selberg L-value
By Miljan Brakovcevi'c. 2010
51 citations recorded by the source corpus.
Let M be an imaginary quadratic field, f a Hecke eigen-cusp form on GL2(Q)\GL2(A) and π̂f the unitary base-change to M of automorphic representation πf associated to f . Take a unitary arithmetic Hecke character χ of M×\M A inducing the inverse of the central character of πf . The celebrated formula of Waldspurger relates the square of Lχ(f) := ∫ M×\M A f(t)χ(t)d×t to the central critical value L( 1 2 , π̂f ⊗ χ). We construct a new p-adic L-function that interpolates Lχ(f) over arithmetic χ’s for a cusp form f in the spirit of the landmark result of Katz where he did that for Eisenstein series.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/30db70ecfef44b388482b5023ec1817865bf058a
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- A converse to a theorem of Gross, Zagier, and Kolyvagin (2014, background): “That they belong to the Iwasawa algebra (which follows from the constructions in [7] and [26]) requires additional argument, essentially extending the formulas to characters ramified at primes above p as is done in [5].”