STNB2019 (33è any)

Pullbacks of Siegel forms and algebraicity of L-values (with a view to p-adic L-functions)


Carlos de Vera Piquero


I will report on an explicit central value formula for a complex L-series of degree 6 associated with a pair of cuspidal Hecke eigenforms f and g of weights 2k and k+1, respectively. Namely, the L-series associated with the tensor product of the Galois representation attached to f and the symmetric square of the one attached to g. Such formula involves the pullback of a Siegel cusp form associated with f (its Saito--Kurokawa lift), and allows us to prove the algebraicity of the central L-value up to the relevant period as predicted by Deligne's conjecture. One of the interests in this central value formula is the construction of a p-adic L-function that would arise as a factor of the triple product p-adic L-function associated with a triple of Hida families (F,G,G). This is joint work with Aprameyo Pal (Essen) and Daniele Casazza (ICMAT).


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