Infinite products in number theory and geometry

TL;DR

This paper introduces Borcherds products and explores their applications in number theory and geometry, particularly in understanding the structure of Hilbert modular surfaces.

Contribution

It provides an accessible introduction to Borcherds products and demonstrates their utility in geometric and number theoretic contexts.

Findings

Borcherds products link automorphic forms to geometric structures.

Applications include insights into Hilbert modular surfaces.

The paper highlights new methods for studying modular varieties.

Abstract

We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces.