# Regularized theta lifts and currents on products of Shimura curves

• Luis Garcia (Imperial)
• Tuesday 27 May 2014, 16:15-17:15
• MR13.

Consider two different holomorphic Hecke eigenforms $f_i \in \pi_i$, $i=1,2$ of weight $2$ on a Shimura curve $X$ over a totally real field $F$. We will first discuss Beilinson’s conjecture relating the image of the complex regulator map from a higher Chow group with the special value of $L(\pi_1 \times \pi_2,s)$ at $s=0$. Then we will review Bruinier´s construction of meromorphic functions on $X$ with divisors supported on CM points. Finally we will show how to use theta lifts of cusp forms on $Sp_4(\mathbb{A}_F)$ to compute, assuming that the $f_i$ have full level and up to an archimedean zeta integral, the period integrals arising as regulators of higher Chow cycles constructed using Bruinier’s functions.

This talk is part of the Number Theory Seminar series.