6 citations · 28 across the 13 of their papers we have counts for
13 papers
Sigma function associated with a hyperelliptic curve with two points at infinity
Takanori Ayano, Victor M. Buchstaber
Baker constructed basic meromorphic functions on the Jacobian variety of a hyperelliptic curve with two points at infinity. We call them Baker functions. The construction is based…
Hyperelliptic sigma functions and the Kadomtsev-Petviashvili equation
Takanori Ayano, Victor M. Buchstaber
In this paper, a theory of hyperelliptic functions based on multidimensional sigma functions is developed and explicit formulas for hyperelliptic solutions to the Kadomtsev-Petvias…
Reduction of bielliptic hyperelliptic functions of genus 3
Takanori Ayano
The present paper is devoted to the problem about the reduction of hyperelliptic functions of genus 3. Our research was motivated by applications to the theory of equations and dyn…
Difference of solutions for the inversion problem of ultra-elliptic integrals
Takanori Ayano
Let be a hyperelliptic curve of genus 2 defined by , where is a polynomial of degree 5. The sigma function associated with is a holomorphic function on $\m…
Hurwitz integrality of the power series expansion of the sigma function for a telescopic curve
Takanori Ayano
A telescopic curve is a certain algebraic curve defined by equations in the affine space of dimension , which can be a hyperelliptic curve and an curve as a specia…
Relationships Between Hyperelliptic Functions of Genus 2 and Elliptic Functions
Takanori Ayano, Victor M. Buchstaber
The article is devoted to the classical problems about the relationships between elliptic functions and hyperelliptic functions of genus 2. It contains new results, as well as a de…
Analytical and number-theoretical properties of the two-dimensional sigma function
Takanori Ayano, Victor M. Buchstaber
This survey is devoted to the classical and modern problems related to the entire function , defined by a family of nonsingular algebraic curves of genus , where…
The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications
Takanori Ayano, Victor Buchstaber
The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus is described in terms of the gradient of it's sigma function. Solutions of corresponding…
Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3
Takanori Ayano, Victor Buchstaber
Buchstaber and Mikhailov introduced the polynomial dynamical systems in with two polynomial integrals on the basis of commuting vector fields on the symmetric square…
On Jacobi Inversion Formulae for Telescopic Curves
Takanori Ayano
For a hyperelliptic curve of genus , it is well known that the symmetric products of points on the curve are expressed in terms of their Abel-Jacobi image by the hyperellipt…
On Addition Formulae for Sigma Functions of Telescopic Curves
Takanori Ayano, Atsushi Nakayashiki
A telescopic curve is a certain algebraic curve defined by equations in the affine space of dimension , which can be a hyperelliptic curve and an curve as a specia…
Sigma Functions for Telescopic Curves
Takanori Ayano
In this paper, we consider the sigma functions for algebraic curves expressed by a canonical form using a finite sequence of positive integers whose greatest common…
Rates of convergence for nearest neighbor estimators with the smoother regression function
Takanori Ayano
In regression analysis one wants to estimate the regression function from a data. In this paper we consider the rate of convergence for the nearest neighbor estimator in case that…