We show that the $p$-adic L-function associated to the tensor square of a $p$-ordinary eigenform factors as the product of the symmetric square $p$-adic L-function of the form with a Kubota-Leopoldt $p$-adic L-function. Our method of proof follows that of Gross, who proved a factorization for Katz's $ p$-adic L-function for a character arising as the restriction of a Dirichlet character. We prove certain special value formulae for classical and $p$-adicRankin L-series at non-critical points. The formula of Bertolini, Darmon, and Rotger in the $p$-adic setting is a key element of our proof. As demonstrated by Citro, we obtain as a corollary of our main result a proof of the exceptional zero conjecture of Greenberg for the symmetric square.
Seminar series
Date
Thu, 27 Sep 2012
Time
16:00 -
17:00
Location
L1
Speaker
Samit Dasgupta
Organisation
UCSC