Abelian functions for trigonal curves of genus three

J. C. Eilbeck; V. Z. Enolski; S. Matsutani; Y. Ônishi; E. Previato

doi:10.1093/imrn/rnm140

Abelian functions for trigonal curves of genus three

J. C. Eilbeck, V. Z. Enolski, S. Matsutani, Y. Ônishi, E. Previato

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Abstract

We develop the theory of generalized Weierstrass s- and P-functions defined on a general trigonal curve of genus three. In particular, we give a list of the associated partial differential equations satisfied by the P-functions, a proof that the coefficients of the power series expansion of the s-function are polynomials of coefficients of the defining equation of the curve, and the derivation of two addition formulae. © The Author 2007.

Original language	English
Article number	rnm140
Journal	International Mathematics Research Notices
Volume	2007
DOIs	https://doi.org/10.1093/imrn/rnm140
Publication status	Published - 2007

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title = "Abelian functions for trigonal curves of genus three",

abstract = "We develop the theory of generalized Weierstrass s- and P-functions defined on a general trigonal curve of genus three. In particular, we give a list of the associated partial differential equations satisfied by the P-functions, a proof that the coefficients of the power series expansion of the s-function are polynomials of coefficients of the defining equation of the curve, and the derivation of two addition formulae. {\textcopyright} The Author 2007.",

author = "Eilbeck, {J. C.} and Enolski, {V. Z.} and S. Matsutani and Y. {\^O}nishi and E. Previato",

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journal = "International Mathematics Research Notices",

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AU - Eilbeck, J. C.

AU - Enolski, V. Z.

AU - Matsutani, S.

AU - Ônishi, Y.

AU - Previato, E.

PY - 2007

Y1 - 2007

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AB - We develop the theory of generalized Weierstrass s- and P-functions defined on a general trigonal curve of genus three. In particular, we give a list of the associated partial differential equations satisfied by the P-functions, a proof that the coefficients of the power series expansion of the s-function are polynomials of coefficients of the defining equation of the curve, and the derivation of two addition formulae. © The Author 2007.

U2 - 10.1093/imrn/rnm140

DO - 10.1093/imrn/rnm140

M3 - Article

SN - 1073-7928

VL - 2007

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

M1 - rnm140

ER -

Abelian functions for trigonal curves of genus three

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