Archimedean arithmetic Siegel--Weil formula for general weights over Shimura curves

TL;DR

This paper establishes an averaging formula for archimedean height pairings of special divisors on Shimura curves, linking it to derivatives of Whittaker functions, advancing understanding in arithmetic geometry.

Contribution

It introduces a new averaging formula for height pairings on Shimura curves involving derivatives of Whittaker functions, applicable to general weights.

Findings

Proves an explicit averaging formula for archimedean height pairings.

Connects height pairings to derivatives of Whittaker functions.

Enhances tools for studying special divisors on Shimura curves.

Abstract

We prove an averaging formula for the canonical archimedean height pairing of special divisors with weights over orthogonal and unitary Shimura curves in terms of derivatives of Whittaker functions.