Volume 25, Issue 1, February 2018, Pages 86 - 105
Rosenhain-Thomae formulae for higher genera hyperelliptic curves
Authors
Keno Eilers
Faculty of Mathematics, University of Oldenburg, Carl-von-Ossietzky-Str. 9-11, 26129 Oldenburg, Germany,keno.eilers@uni-oldenburg.de
Received 2 August 2017, Accepted 7 September 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2018.1440744How to use a DOI?
- Keywords
- Theta Functions; Rosenhain formula; Thomae Formula
- Abstract
Rosenhain's famous formula expresses the periods of first kind integrals of genus two hyperelliptic curves in terms of θ-constants. In this paper we generalize the Rosenhain formula to higher genera hyperelliptic curves by means of the second Thomae formula for derivative non-singular θ-constants.
- Copyright
- © 2018 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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TY - JOUR AU - Keno Eilers PY - 2021 DA - 2021/01/06 TI - Rosenhain-Thomae formulae for higher genera hyperelliptic curves JO - Journal of Nonlinear Mathematical Physics SP - 86 EP - 105 VL - 25 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2018.1440744 DO - 10.1080/14029251.2018.1440744 ID - Eilers2021 ER -