This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real
fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series …

In this article, we improve our main results from [LL21] in two directions: First, we allow
ramified places in the CM extension at which we consider representations that are spherical …

We study a partially linearized version of the relative trace formula for the arithmetic Gan--
Gross--Prasad conjecture for the unitary group U(V). The linear factor in this relative trace …

We form generating series of special divisors, valued in the Chow group and in the
arithmetic Chow group, on the compactified integral model of a Shimura variety associated …

We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry
condition. They are formal analogs of Fourier–Jacobi expansions of Siegel modular forms …

Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real
signature and constructed in some instances via a $ p $-adic analogue of Borcherds' …

The main goal of this expository article is to survey recent progress on the arithmetic Siegel–
Weil formula and its applications. We begin with the classical sum of two squares problem …

We prove the arithmetic inner product formula conjectured in the first paper of this series for
n= 1, that is, for the group U (1, 1) F unconditionally. The formula relates central L-derivatives …

For any unramified quadratic extension of $ p $-adic local fields $ F/F_0 $$(p> 2) $, we
formulate several arithmetic transfer conjectures at any maximal parahoric level, in the …

We prove the Arithmetic Fundamental Lemma conjecture over a general p-adic field with
odd residue cardinality q dimV. Our strategy is similar to the one used by the second author …