## STNB2019 (33rd edition)

### A Gross--Zagier trace formula for product of theta series.

#### Presenters

Óscar Rivero Salgado

#### Abstract

In this talk, we give some ingredients used by Darmon--Harris--Rotger--Venkatesh in their proof of Harris--Venkatesh's conjecture for dihedral modular forms. The main result is a computation of the trace of the product of two cuspidal theta series attached to ray class characters of the same quadratic field $K$ via the Weil representation. When $K$ is imaginary, this trace is expressed in terms of an inner product on a definite quaternion algebra, making use of a theta correspondence.

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