# Computing Theta Functions with Julia

## TL;DR

The paper introduces Theta.jl, a Julia package for accurate and efficient numerical computation of Riemann theta functions and their derivatives, optimized for repeated evaluations in small dimensions.

## Contribution

It provides a new Julia package that enables precise and fast computation of theta functions with characteristics, including derivatives, tailored for small-dimensional problems.

## Key findings

- Efficient implementation of theta function evaluations in Julia.
- Application to the Schottky problem in genus five.
- Optimized for multiple evaluations with the same Riemann matrix.

## Abstract

We present a new package Theta.jl for computing with the Riemann theta function. It is implemented in Julia and offers accurate numerical evaluation of theta functions with characteristics and their derivatives of arbitrary order. Our package is optimized for multiple evaluations of theta functions for the same Riemann matrix, in small dimensions. As an application, we report on experimental approaches to the Schottky problem in genus five.