# Off-diagonal estimates of the Bergman kernel on hyperbolic Riemann surfaces of finite volume

## TL;DR

This paper derives off-diagonal estimates for the Bergman kernel on hyperbolic Riemann surfaces of finite volume, providing insights into the kernel's behavior away from the diagonal.

## Contribution

It introduces new off-diagonal estimates for the Bergman kernel on hyperbolic Riemann surfaces of finite volume, extending previous diagonal results.

## Key findings

- Derived explicit off-diagonal bounds for the Bergman kernel
- Extended understanding of kernel decay properties on hyperbolic surfaces
- Applicable to tensor products of the cotangent line bundle

## Abstract

In this article, we derive off-diagonal estimates of the Bergman kernel associated to tensor- products of the cotangent line bundle defined over a hyperbolic Riemann surface of finite volume.