Rosenhain-Thomae formulae for higher genera hyperelliptic curves

DOI10.1080/14029251.2018.1440744zbMath1420.14069arXiv1707.08855OpenAlexW2963606680MaRDI QIDQ5231112

Keno Eilers

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08855

zbMATH Keywords

Theta functionsrosenhain formulathomae formula

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Theta functions and abelian varieties (14K25) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Theta functions and curves; Schottky problem (14H42)

Related Items (5)

Genus two Siegel quasi-modular forms and Gromov-Witten theory of toric Calabi-Yau threefolds ⋮ General derivative Thomae formula for singular half-periods ⋮ Elliptic loci of \(\mathrm{SU}(3)\) vacua ⋮ Thomae's derivative formulae for trigonal curves ⋮ A generalization of Jacobi's derivative formula to dimension two, II

Cites Work

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• A generalization of Rosenhain's normal form for hyperelliptic curves with an application
• Theta functions on Riemann surfaces
• Reduction of abelian functions and algebraically integrable systems. I
• Inversion of a general hyperelliptic integral and particle motion in Hořava–Lifshitz black hole space-times
• Weber's formula for the bitangents of a smooth plane quartic
• A new proof of a Thomae-like formulafor non hyperelliptic genus 3 curves
• Periods of hyperelliptic integrals expressed in terms of θ -constants by means of Thomae formulae

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