Determinant Expressions for Hyperelliptic Functions

Determinant Expressions for Hyperelliptic Functions in Genus Three

The Addition Law Attached to a Stratification of a Hyperelliptic Jacobian Variety

This article shows explicit relation between fractional expressions of Schottky-Klein type for hyperelliptic σ-function and a product of differences of the algebraic coordinates on each stratum of natural stratification in a hyperelliptic Jacobian.

Uvw Relations over a Subvariety of a Hyperelliptic Jacobian

This article extends relations of Mumford’s UV W -expressions to those in subvariety in a hyperelliptic Jacobian using Baker’s method.

A pr 2 00 2 Determinant Expressions for Hyperelliptic Functions ( with an Appendix by Shigeki Matsutani )

Although this formula can be obtained by a limiting process from (0.1), it was found before [FS] by the paper of Kiepert [K]. If we set y(u) = 12℘ ′(u) and x(u) = ℘(u), then we have an equation y(u) = x(u)+ · · · , that is a defining equation of the elliptic curve to which the functions ℘(u) and σ(u) are attached. Here the complex number u and the coordinate (x(u), y(u)) correspond by the equality

Determinant Expressions for Hyperelliptic Functions ( with an Appendix by Shigeki Matsutani ) Yoshihiro

Although this formula can be obtained by a limiting process from (0.1), it was found before [FS] by the paper of Kiepert [K]. If we set y(u) = 12℘ ′(u) and x(u) = ℘(u), then we have an equation y(u) = x(u)+ · · · , that is a defining equation of the elliptic curve to which the functions ℘(u) and σ(u) are attached. Here the complex number u and the coordinate (x(u), y(u)) correspond by the equality

1 5 Ju n 20 04 DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS ( with an Appendix by Shigeki Matsutani ) YOSHIHIRO ÔNISHI

Although this formula can be obtained by a limiting process from (0.1), it was found before [11] by the paper of Kiepert [13]. If we set y(u) = 1 2℘ ′(u) and x(u) = ℘(u), then we have an equation y(u) = x(u)+ · · · , that is a defining equation of the elliptic curve to which the functions ℘(u) and σ(u) are attached. Here the complex number u and the coordinate (x(u), y(u)) correspond by the equ...