Article contents
Computing theta functions in quasi-linear time in genus two and above
Published online by Cambridge University Press: 26 August 2016
Abstract
We outline an algorithm to compute $\unicode[STIX]{x1D703}(z,\unicode[STIX]{x1D70F})$ in genus two in quasi-linear time, borrowing ideas from the algorithm for theta constants and the one for
$\unicode[STIX]{x1D703}(z,\unicode[STIX]{x1D70F})$ in genus one. Our implementation shows a large speed-up for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus
$g$.
MSC classification
- Type
- Research Article
- Information
- LMS Journal of Computation and Mathematics , Volume 19 , Special Issue A: Algorithmic Number Theory Symposium XII , 2016 , pp. 163 - 177
- Copyright
- © The Author(s) 2016
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20160907143622272-0774:S1461157016000309_inline4.gif?pub-status=live)
- 6
- Cited by