On Algebraic Expressions of Sigma Functions for (n, s) Curves

نویسنده

  • Atsushi Nakayashiki
چکیده

An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be the Schur function determined from the gap sequence at infinity. ∗e-mail: [email protected]

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Addition Formulae for Sigma Functions of Telescopic Curves

A telescopic curve is a certain algebraic curve defined by m − 1 equations in the affine space of dimension m, which can be a hyperelliptic curve and an (n, s) curve as a special case. We extend the addition formulae for sigma functions of (n, s) curves to those of telescopic curves. The expression of the prime form in terms of the derivative of the sigma function is also given.

متن کامل

The function ring functors of pointfree topology revisited

This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...

متن کامل

On Jacobi Inversion Formulae for Telescopic Curves

For a hyperelliptic curve of genus g, it is well known that the symmetric products of g points on the curve are expressed in terms of their Abel–Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by y = f(x), which are special cases of (n, s) curves, and d...

متن کامل

INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME

A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...

متن کامل

Soliton Solutions of Korteweg-de Vries Equations and Hyperelliptic Sigma Functions

The modern soliton theories [DJKM, SN, SS], which were developed in ending of last century, are known as the infinite dimensional analysis and gave us fruitful and beautiful results, e.g., relations of soliton equations to universal Grassmannian manifold, Plücker embedding, infinite dimensional Lie algebra, loop algebra, representation theories, Schur functions, Young diagram, and so on. They s...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008