HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Computing theta functions in quasi-linear time in genus 2 and above

Hugo Labrande 1, 2 Emmanuel Thomé 1
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We outline an algorithm to compute θ(z, τ) in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for θ(z, τ) in genus 1. Our implementation shows a large speedup for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus g.
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

Contributor : Hugo Labrande Connect in order to contact the contributor
Submitted on : Monday, February 22, 2016 - 11:41:50 AM
Last modification on : Friday, February 4, 2022 - 3:29:48 AM
Long-term archiving on: : Sunday, November 13, 2016 - 12:20:13 AM


Files produced by the author(s)




Hugo Labrande, Emmanuel Thomé. Computing theta functions in quasi-linear time in genus 2 and above. LMS Journal of Computation and Mathematics, London Mathematical Society, 2016, Special issue: Algorithmic Number Theory Symposium XII, 19 (A), pp.163-177. ⟨10.1112/S1461157016000309⟩. ⟨hal-01277169⟩



Record views


Files downloads