DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS

YOSHIHIRO ÔNISHI

doi:10.1017/S0013091503000695

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we give an elegant generalization of the formula of Frobenius–Stickelberger from elliptic curve theory to all hyperelliptic curves. A formula of Kiepert type is also obtained by a limiting process from this generalization. In the appendix a determinant expression of D. G. Cantor is also derived.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

ÔNISHI, Yoshihiro 2004. Determinantal Expressions for Hyperelliptic Functions in Genus Three. Tokyo Journal of Mathematics, Vol. 27, Issue. 2,

MATSUTANI, Shigeki and PREVIATO, Emma 2008. Jacobi inversion on strata of the Jacobian of the C rs curve y r =f(x). Journal of the Mathematical Society of Japan, Vol. 60, Issue. 4,

ENOLSKII, Victor MATSUTANI, Shigeki and ÔNISHI, Yoshihiro 2008. The Addition Law Attached to a Stratification of a Hyperelliptic Jacobian Variety. Tokyo Journal of Mathematics, Vol. 31, Issue. 1,

Eilbeck, J. C. Enolski, V. Z. Matsutani, S. Ônishi, Y. and Previato, E. 2008. Addition formulae over the Jacobian pre-image of hyperelliptic Wirtinger varieties. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2008, Issue. 619,

ÔNISHI, YOSHIHIRO 2009. ABELIAN FUNCTIONS FOR TRIGONAL CURVES OF DEGREE FOUR AND DETERMINANTAL FORMULAE IN PURELY TRIGONAL CASE. International Journal of Mathematics, Vol. 20, Issue. 04, p. 427.

Bunkova, E. Yu. and Buchstaber, V. M. 2009. Heat equations and families of two-dimensional sigma functions. Proceedings of the Steklov Institute of Mathematics, Vol. 266, Issue. 1, p. 1.

Hone, Andrew N.W. 2010. Analytic solutions and integrability for bilinear recurrences of order six. Applicable Analysis, Vol. 89, Issue. 4, p. 473.

Eilbeck, J. C. Enolski, V. Z. Matsutani, S. Onishi, Y. and Previato, E. 2010. Abelian Functions for Trigonal Curves of Genus Three. International Mathematics Research Notices,

Eilbeck, J. C. Matsutani, S. and Ônishi, Y. 2011. Addition formulae for Abelian functions associated with specialized curves. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 369, Issue. 1939, p. 1245.

Uchida, Yukihiro 2011. Division polynomials and canonical local heights on hyperelliptic Jacobians. Manuscripta Mathematica, Vol. 134, Issue. 3-4, p. 273.

Onishi, Yoshihiro 2012. Determinant Formulae in Abelian Functions for a General Trigonal Curve of Degree Five. Computational Methods and Function Theory, Vol. 11, Issue. 2, p. 547.

KOMEDA, JIRYO MATSUTANI, SHIGEKI and PREVIATO, EMMA 2013. THE SIGMA FUNCTION FOR WEIERSTRASS SEMIGROUPS 〈3, 7, 8〉 AND 〈6, 13, 14, 15, 16〉. International Journal of Mathematics, Vol. 24, Issue. 11, p. 1350085.

Uchida, Yukihiro and Uchiyama, Shigenori 2013. Pairing-Based Cryptography – Pairing 2012. Vol. 7708, Issue. , p. 218.

Gibbons, John Matsutani, Shigeki and Ônishi, Yoshihiro 2013. Relationship between the prime form and the sigma function for some cyclic (r,s) curves. Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue. 17, p. 175203.

Nakayashiki, Atsushi and Yori, Keijiro 2013. Symmetries, Integrable Systems and Representations. Vol. 40, Issue. , p. 429.

MATSUTANI, Shigeki and PREVIATO, Emma 2014. Jacobi inversion on strata of the Jacobian of the $C_{rs}$ curve $y^r = f(x)$, II. Journal of the Mathematical Society of Japan, Vol. 66, Issue. 2,

Nakayashiki, Atsushi 2016. Tau Function Approach to Theta Functions. International Mathematics Research Notices, Vol. 2016, Issue. 17, p. 5202.

Ayano, Takanori and Buchstaber, Victor Matveevich 2017. Поле мероморфных функций на сигма-дивизоре гиперэллиптической кривой рода 3 и приложения. Функциональный анализ и его приложения, Vol. 51, Issue. 3, p. 4.

Ayano, T. and Buchstaber, V. M. 2017. The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications. Functional Analysis and Its Applications, Vol. 51, Issue. 3, p. 162.

Bernatska, Julia Enolski, Victor and Nakayashiki, Atsushi 2020. Sato Grassmannian and Degenerate Sigma Function. Communications in Mathematical Physics, Vol. 374, Issue. 2, p. 627.

Download full list

Article contents

DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS

Abstract

Keywords

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests