A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Hyperelliptic Curves with Compact Parameters

2005
*
Designs, Codes and Cryptography
*

We present a family of

doi:10.1007/s10623-004-1718-0
fatcat:kvmx3ihpg5e5vbrlx4clt7bnki
*hyperelliptic**curves*whose Jacobians are suitable for cryptographic use, and whose*parameters*can be specified in a highly efficient way. ... This is done via complex multiplication and identity-based*parameters*. We also present some novel computational shortcuts for these families. ... Introduction In our earlier paper [1] we introduced the notion of elliptic*curves**with**compact**parameters*. ...##
###
Compact Representation of Domain Parameters of Hyperelliptic Curve Cryptosystems
[chapter]

2002
*
Lecture Notes in Computer Science
*

We discussed how to represent the domain

doi:10.1007/3-540-45450-0_17
fatcat:ybgewadea5hlbgkzuonveijhue
*parameters*of HCC in a*compact*way. ... To achieve the same level of security,*hyperelliptic**curve*cryptosystems (HCC) use a smaller field than elliptic*curve*cryptosystems (ECC). ... How to eradicate an*parameter*in the equation of an*hyperelliptic**curve*is also discussed. We also give the number of bits to represent the order of the Jacobian. ...##
###
Period Constraints on Hyperelliptic Branch Points
[article]

2021
*
arXiv
*
pre-print

contain any period matrices of

arXiv:2106.15696v1
fatcat:ko6dwfpxjnem5pymxvgkn2gzau
*hyperelliptic**curves*. ... Information Theoretic analysis of the periods of a*hyperelliptic**curve*provides more information about the well--known but abstract relationship between the branch points and the periods. ... In one direction, suppose that Alice wants to tell Bob about a*compact**curve*(ie, Riemann Surface)*with*genus g ≥ 2. ...##
###
On a conjecture of Whittaker concerning uniformization of hyperelliptic curves

2003
*
Transactions of the American Mathematical Society
*

differential equation

doi:10.1090/s0002-9947-03-03441-x
fatcat:3hzymutglrdovej7ppaeh3fh2e
*with*singularities at the values a i . ... Rankin some twenty years later, were able to prove the conjecture for several families of*hyperelliptic*surfaces, characterized by the fact that they admit a large group of symmetries. ... The family of*curves*y 2 = (x n − 1)(x n − λ) In this section we study the 1-*parameter*family of*hyperelliptic**curves*of genus n − 1 C λ,n = y 2 = (x n − 1)(x n − λ) , λ ∈ R \ {0, 1}, n ≥ 3, whose branching ...##
###
Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions

2001
*
Journal of Physics A: Mathematical and General
*

Explicit function forms of

doi:10.1088/0305-4470/34/22/312
fatcat:w7w5wrpln5cxzn2iut7wfq3cxa
*hyperelliptic*solutions of Korteweg-de Vries (KdV) and Kadomtsev-Petviashvili (KP) equations were constructed for a given*curve*y^2 = f(x) whose genus is three. ... Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator D, identities of Pfaffians, symmetric functions,*hyperelliptic*σ-function and -functions; _μν = -∂_μ∂_νσ ... Although we will mainly deal*with*a*curve**with*genus three, we will give definitions and expressions of*hyperelliptic**curves**with*general genus for later convenience. Notation 1. ...##
###
On the structure of the Whittaker sublocus of the moduli space of algebraic curves

2006
*
Proceedings of the Royal Society of Edinburgh. Section A Mathematics
*

This is the subset of points representing

doi:10.1017/s0308210500004583
fatcat:waigunffprdnrddl3y254ofdwi
*hyperelliptic**curves*which satisfy Whittaker's conjecture on the uniformization of*hyperelliptic**curves*via monodromy of Fuchsian differential equations. ... MS received ; ) We prove the*compactness*of Whittaker sublocus of moduli space of Riemann surfaces (complex algebraic*curves*). ... sphereĈ = C∪{∞}, as a*hyperelliptic*algebraic*curve*. ...##
###
Page 8704 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

++,A2¢42 are branch points on the

*hyperelliptic**curve*&, and W% is a g xg matrix of a-periods of nonnormalized holomorphic differentials on this*curve*. ... Summary: “A*compact*Riemann surface X of genus g is called an (M — 1)-surface if it admits an anticonformal involution that fixes g simple closed*curves*, the second maximum number by Harnack’s theorem. ...##
###
Page 74 of Mathematical Reviews Vol. 51, Issue 1
[page]

1976
*
Mathematical Reviews
*

3 or |L|=|2B+I'|, where B is an irreducible

*curve*of genus 2 and I a rational*curve**with*B['=1. ... 24 then either (i) F contains an irreducible*curve*E*with*E-L=2 and arithmetic genus | or (ii) F contains an irreducible*curve*B*with*|L| =|2B| and arithmetic genus 2. ...##
###
Page 2514 of Mathematical Reviews Vol. , Issue 2000d
[page]

2000
*
Mathematical Reviews
*

Let M be an elliptic-

*hyperelliptic**compact*Riemann surface of genus at least 4. ... The problem studied in this paper is the construction of meromor- phic homomorphisms between flat vector bundles over*compact*Riemann surfaces*with*prescribed zeros and poles (*with*multiplic- ities). ...##
###
Construction of Hyperbolic Signal Sets from the Uniformization of Hyperelliptic Curves
[article]

2020
*
arXiv
*
pre-print

of the tessellation p,q and the degree of the

arXiv:2009.05563v1
fatcat:dms6rybbarb6rekg2nen4x4jeu
*hyperelliptic**curve*is established. ... In this paper, we present a new approach to the problem of designing hyperbolic signal sets matched to groups by use of Whittaker's proposal in the uniformization of*hyperelliptic**curves*via Fuchsian differential ... of the Fuchsian subgroup associated*with*the fundamental region which uniformizes the given*hyperelliptic**curve*; • To establish a relation between the degree of the*hyperelliptic**curve*and the*parameters*...##
###
The Deligne–Mumford and the Incidence Variety Compactifications of the Strata of \Omega \protect \mathcal{M}_{g}

2018
*
Annales de l'Institut Fourier
*

of

doi:10.5802/aif.3187
fatcat:anxlj7wnfvaircgvqmu2zcvqua
*compact*type. ... We study in detail the compactifications of the*hyperelliptic*minimal strata and of the odd minimal stratum in genus three. ... In fact, since*hyperelliptic**curves*are covers of degree two above a*curve*of*compact*type, many ideas will work in this case. Proof. ...##
###
Introduction to Compact Riemann Surfaces
[chapter]

2010
*
Lecture notes in mathematics
*

*Hyperelliptic*Riemann surfaces Let R be a

*compact*Riemann surface of a

*hyperelliptic*

*curve*as in Theorem 1. ... The Riemann surface C can be made a

*compact*Riemann surfacê

*Hyperelliptic*

*curves*. ...

##
###
Page 191 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

Finally, he deals

*with*equations of*hyperelliptic*surfaces of Belyi type. ... Fi- nally, the correct reference concerning the classification of groups of automorphisms of*hyperelliptic*Riemann surfaces is not the re- viewer’s monograph [Groups of automorphisms of*compact*Riemann ...##
###
A Connection Between Geometry and Dynamical Systems

2005
*
Journal of Dynamical Systems and Geometric Theories
*

*curve*of genus 2. e) We show that at some special values of the

*parameters*λ 1 and λ 2 , we can describe elliptic solutions which are associated

*with*two-gap elliptic solitons of the Korteweg-de Vries ... This paper deals

*with*a geometric and systematic approach to the integration of a nonlinear dynamical system: the anisotropic harmonic oscillator in a radial quartic potential. ... Since Γ is

*hyperelliptic*of genus 2, it has 6 distinct Weierstrass points (Indeed, suppose C is a smooth

*hyperelliptic*

*curve*of genus g ≥ 2

*with*: C → P 1 (C) the two-sheeted map, then all the branch points ...

##
###
Information Theory and Moduli of Riemann Surfaces
[article]

2013
*
arXiv
*
pre-print

The results here show that,

arXiv:1309.2304v1
fatcat:hdzhrzrionecdo4ijkx7ejwt4i
*with*high probability, any set of 3g-3 periods form moduli for the surface. ... One interpretation of Torelli's Theorem, which asserts that a*compact*Riemann Surface X of genus g > 1 is determined by the g(g+1)/2 entries of the period matrix, is that the period matrix is a message ... Now suppose that Alyce wants to describe a*compact*Riemann surface*with*genus g > 1 to Bob. ...
« Previous

*Showing results 1 — 15 out of 2,885 results*