Arithmetical Power Series Expansion of the Sigma Function for a Plane Curve

DOI10.1017/S0013091517000463zbMath1472.11186OpenAlexW2809440398MaRDI QIDQ5228185

Yoshihiro Ônishi

Publication date: 9 August 2019

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091517000463

zbMATH Keywords

abelian functionshigher genus curvesHurwitz integralitygeneralized sigma functions

Mathematics Subject Classification ID

Plane and space curves (14H50) Abelian varieties of dimension (> 1) (11G10) Theta functions and abelian varieties (14K25) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (3)

Аналитические и теоретико-числовые свойства двумерных сигма-функций ⋮ The sigma function over a family of curves with a singular fiber ⋮ Complementary modules of Weierstrass canonical forms

Cites Work

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• On algebraic expressions of sigma functions for (\(n, s\)) curves
• Fonctions thêta et théorème du cube
• Algebraic theta functions and the \(p\)-adic interpolation of Eisenstein-Kronecker numbers
• The \(p\)-adic sigma function
• Theta functions on Riemann surfaces
• Sigma functions for telescopic curves
• Computation of \(p\)-adic heights and log convergence
• Heat equations in a nonholomic frame
• Sigma Function as A Tau Function

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