Vol. 11, No. 1, 2021

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Computing theta functions with Julia

Daniele Agostini and Lynn Chua

Vol. 11 (2021), 41–51
DOI: 10.2140/jsag.2021.11.41
Abstract

We present a new package Theta.jl for computing 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 5.

Keywords
theta function, numerical, Julia, abelian varieties, Riemann surfaces, Schottky problem, Jacobian
Mathematical Subject Classification 2010
Primary: 14-04, 14H42, 14K25, 32-04, 65E99
Supplementary material

A Julia package for computing the Riemann theta function and its derivatives.

Milestones
Received: 21 February 2020
Revised: 21 October 2020
Accepted: 9 November 2020
Published: 16 March 2021
Authors
Daniele Agostini
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Leipzig
Germany
Lynn Chua
Department of Computing and Mathematical Sciences
California Institute of Technology
Pasadena, CA
United States