A generalization of Rosenhain's normal form for hyperelliptic curves with an application

@inproceedings{Takase1996AGO,
  title={A generalization of Rosenhain's normal form for hyperelliptic curves with an application},
  author={Koichi Y. Takase},
  year={1996}
}
  • K. Takase
  • Published 1 September 1996
  • Mathematics
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15 Citations
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15 Citations

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Periods of hyperelliptic integrals expressed in terms of theta-constants by means of Thomae formulae.
  • V. Enolski, P. Richter
  • Mathematics
    Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
  • 2008
Expressions for the periods of first- and second-kind integrals on hyperelliptic curves are given in terms of theta-constants. They are derived with the help of Thomae's classical formulae and…
Periods of hyperelliptic integrals expressed in terms of θ-constants by means of Thomae formulae
  • V. Enolski, P. Richter
  • Mathematics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2007
Expressions for the periods of first- and second-kind integrals on hyperelliptic curves are given in terms of θ-constants. They are derived with the help of Thomae's classical formulae and…
Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves
Nous proposons une solution au probleme de Schottky hyperelliptique. Celle-ci est basee sur l'utilisation de matrices jacobiennes de fonctions theta et de modeles symetriques pour les courbes…
An inverse Jacobian algorithm for Picard curves
We study the inverse Jacobian problem for the case of Picard curves over $${\mathbb {C}}$$ C . More precisely, we elaborate on an algorithm that, given a small period matrix $$\varOmega \in…
On different expressions for invariants of hyperelliptic curves of genus 3
TLDR
Under certain conditions on its jacobian, this paper gives a criterion for determining the type of bad reduction of a genus 3 hyperelliptic curve and gets Shioda invariants described in terms of differences of roots of the equation defining the hyperellipic curve.
Genus 3 hyperelliptic curves with CM via Shimura reciprocity
Up to isomorphism over C, every simple principally polarized abelian variety of dimension 3 is the Jacobian of a smooth projective curve of genus 3. Furthermore, this curve is either a hyperelliptic…
Inverse Jacobian and related topics for certain superelliptic curves
Given an elliptic curve E over the complex numbers (CC) given by y^2 = x^3 + ax + b, there exists a lattice L in CC such that the group E(CC) of complex points on E is isomorphic to the complex…
Rosenhain-Thomae formulae for higher genera hyperelliptic curves
Rosenhain's famous formula expresses the periods of first kind integrals of genus two hyperelliptic curves in terms of θ-constants. In this paper we generalize the Rosenhain formula to higher genera…
Constructing genus 3 hyperelliptic Jacobians with CM
TLDR
An algorithm which works in complete generality, for any CM sextic field, and computes minimal polynomials of the Rosenhain invariants for any period matrix of the Jacobian is given.
A new proof of a Thomae-like formula for non hyperelliptic genus 3 curves
We discuss Weber's formula which gives the quotient of two Thetanullwerte for a plane smooth quartic in terms of the bitangents. In particular, we show how it can easily be derived from the…
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References

SHOWING 1-2 OF 2 REFERENCES
Tata Lectures on Theta I
and motivation: theta functions in one variable.- Basic results on theta functions in several variables.
Ostwald's Klassiker der Exacten Wissenschaften
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