Twisted triple product p-adic L-functions and Hirzebruch-Zagier cycles

Abstract

Let $L/F$ be a quadratic extension of totally real number fields. For any prime $p$ unramified in $L$, we construct a $p$-adic $L$-function interpolating the central values of the twisted triple product $L$-functions attached to a $p$-nearly ordinary family of unitary cuspidal automorphic representations of ${\text{Res}}_{L\times F/F}({\text{GL}}_2)$. Furthermore, when $L/\mathbb{Q}$ is a real quadratic number field and $p$ is a split prime, we prove a $p$-adic Gross-Zagier formula relating the value of the $p$-adic $L$-function outside the range of interpolation to the syntomic Abel-Jacobi image of generalized Hirzebruch-Zagier cycles.

To appear in J. Inst. Math. Jussieu incorporating many useful comments of the referee. We advice the interested reader to use the published version

References in corpus (1)

• Hirzebruch-Zagier cycles and twisted triple product Selmer groups

Cited by in corpus (2)

• The universal $p$-adic Gross-Zagier formula
• Syntomic regulators of Asai--Flach classes