Computing Hilbert modular forms as orthogonal modular forms

TL;DR

This paper presents an efficient method to compute Hilbert modular forms by representing them as orthogonal modular forms, extending Birch's approach to a broader context.

Contribution

It introduces a generalized technique for computing Hilbert modular forms using orthogonal modular forms, expanding upon Birch's original method.

Findings

Enhanced computational efficiency for Hilbert modular forms

Generalization of Birch's method to broader cases

Potential applications in number theory and algebraic geometry

Abstract

We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.