相关论文: Reduction of bielliptic hyperelliptic functions of…
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 derivation from them of well-known results on these issues.…
We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We…
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These…
We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic $\sigma$-function. These functions are related to weight 2 $\theta$-functions in the same fashion as…
We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and an advancement of efficient symbolic computation techniques has allowed for recent progress in this area. In this paper we focus…
For each group $G$, $(|G| > 2)$ \, which acts as a full automorphism group on a genus 3 hyperelliptic curve, we determine the family of curves which have 2-Weierstrass points. Such families of curves are explicitly determined in terms of…
In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary oc-tics to Siegel modular forms of genus 3. We use this connection to show that certain modular…
In this work we give an explicit solution to the problem of differentiation of hyperelliptic functions in genus $3$ case. It is a genus $3$ analogue of the result of F. G. Frobenius and L. Stickelberger. Our method is based on the series of…
We study degree 2 and 4 elliptic subcovers of hyperelliptic curves of genus 3 defined over $\mathbb C$. The family of genus 3 hyperelliptic curves which have a degree 2 cover to an elliptic curve $E$ and degree 4 covers to elliptic curves…
We show that for any elliptic curve (with j invariant not 0 or 1728) over any field of characteristic different from 2 and 3, there exists an hyperelliptic curve H of genus 5 with two independent maps to the given elliptic curve. We also…
We consider the generalized dual transformation for elliptic/hyperelliptic $\wp$ functions up to genus three. For the genus one case, from the algebraic addition formula, we deduce that the Weierstrass $\wp$ function has the SO(2,1) $\cong$…
In this paper we study genus 2 function fields K with degree 3 elliptic subfields. We show that the number of Aut(K)-classes of such subfields of K is 0,1,2, or 4. Also we compute an equation for the locus of such K in the moduli space of…
In this paper we consider models for genus one curves of degree n for n = 2, 3 and 4, which arise in explicit n-descent on elliptic curves. We prove theorems on the existence of minimal models with the same invariants as the minimal model…
We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of genus one and two with many automorphisms. In the genus one case we find new addition formulae for the equianharmonic and lemniscate…
We study genus 3 hyperelliptic curves which have an extra involution. The locus $\L_3$ of these curves is a 3-dimensional subvariety in the genus 3 hyperelliptic moduli $\H_3$. We find a birational parametrization of this locus by affine…
The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of a holomorphic hyperelliptic integral. The result of the inversion is…
We consider the problem of efficient computation in the Jacobian of a hyperelliptic curve of genus 3 defined over a field whose characteristic is not 2. For curves with a rational Weierstrass point, fast explicit formulas are well known and…
We study genus 2 function fields with elliptic subfields of degree 2. The locus $\L_2$ of these fields is a 2-dimensional subvariety of the moduli space $\mathcal M_2$ of genus 2 fields. An equation for $\L_2$ is already in the work of…
In this work we give an explicit solution to the problem of differentiation of hyperelliptic functions in genus $4$ case. It is a genus $4$ analogue of the classical result of F. G. Frobenius and L. Stickelberger [F. G. Frobenius, L.…
The maximal cut of the nonplanar crossed box diagram with all massive internal propagators was long ago shown to encode a hyperelliptic curve of genus 3 in momentum space. Surprisingly, in Baikov representation, the maximal cut of this…