STNB2020(34th edition)

p-adic families of d-th Shintani liftings

Presenters

Carlos de Vera Piquero

Abstract

As a variant of the original Shintani lifting from integral weight modular forms to half-integral weight modular forms, Kohnen studied in detail similar liftings associated with a choice of a fundamental discriminant $d$, realizing the Shimura--Shintani correspondence. These have moreover the advantage of describing precisely the relation between Fourier coefficients of half-integral weight modular forms and special values of twisted L-series associated to (integral weight) modular forms. In this talk I will describe a construction of the $d$-th Shintani lifting of a Hida family of ordinary $p$-stabilized newforms, interpolating the $d$-th Shintani liftings of its classical specializations. As a consequence, we derive a $\Lambda$-adic Kohnen formula interpreting Fourier coefficients of this lifting as $p$-adic $L$-functions. This is joint work with Daniele Casazza.