Computing theta functions with Julia. (English) Zbl 1483.14002

Agostini, Daniele; Chua, Lynn

J. Softw. Algebra Geom. 11, 41-51 (2021).

Summary: 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.

MSC:

14-04	Software, source code, etc. for problems pertaining to algebraic geometry
14H42	Theta functions and curves; Schottky problem
14K25	Theta functions and abelian varieties
32-04	Software, source code, etc. for problems pertaining to several complex variables and analytic spaces
65E99	Numerical methods in complex analysis (potential theory, etc.)

Keywords:

theta function; numerical; abelian varieties; Riemann surfaces; Schottky problem; Jacobian

Software:

SageMath; Julia; Theta.jl; RiemannSurface

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