Hyperelliptic Curves
Bounds of the rank of the Mordell–Weil group of Jacobians of Hyperelliptic Curves
... to curves of genus g ≥ 2. In order to find other families of hyperelliptic curves of genus g ≥ 2 where a similar bound applies, we use a method of 2-descent for jacobians described by Cassels, ...
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FROM TOPOLOGICAL RECURSION TO WAVE FUNCTIONS AND PDES QUANTIZING HYPERELLIPTIC CURVES
... spectral curves with a global involution satisfy a system of partial differential equations, whose equations can be seen as quantizations of the original spectral ...spectral curves can be parametrized with ...
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Hardware and Arithmetic for Hyperelliptic Curves Cryptography
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...
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Hardware and Arithmetic for Hyperelliptic Curves Cryptography
... The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au[r] ...
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Coleman integration for hyperelliptic curves : algorithms and applications
... Motivating these algorithms is the fact that Coleman integration plays an impor- tant role in a study of the arithmetic of curves and abelian varieties. For examp[r] ...
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The rank of hyperelliptic Jacobians in families of quadratic twists
... equal) hyperelliptic curves C 1 , C 2 , · · · , C s over k, is there a hyperelliptic curve C/k such that J C ∼ JC1 × · · · × J Cs × B for some abelian variety B/k? As mentioned in the introduction, ...
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Rational points on curves
... ‘reasonable’ curves of genus 2, generators of a finite-index subgroup of J (Q) can usually be ...For hyperelliptic curves of genus at least 3, it may still be possible in many cases, but the ...
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Very special divisors on real algebraic curves
... Remark 4.4 In the situation of Theorem 4.1, if in addition the genus of X ′ is 0, then X is an hyperelliptic curve with δ(g 1 2 ) = 2 and |D| = rg 2 1 with r odd. Such hyperelliptic curves exist (see ...
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An effective proof of the hyperelliptic Shafarevich conjecture
... curves over K of Coates [5] and of Fuchs, Wüstholz and the author ...of hyperelliptic curves over K of genus g with good reduction out- side ...for hyperelliptic curves over ...
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Group actions on dendrites and curves
... a probability measure. This is natural since S 1 is homogeneous (as is the Menger curve [1, Thm. III], but no other curve [2, Thm. XIII]). It is also compatible with the case of dendrites by Proposition 3.2. However, our ...
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CURVES IN HILBERT MODULAR VARIETIES
... rational curves not contained in the boundary ...entire curves into Hilbert modular varieties, generalizing previous works [Tib15] which dealt with the surface ...
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Huff's Model for Elliptic Curves
... This paper extends and generalizes Huff’s model. It presents fast ex- plicit formulæ for point addition and doubling on Huff curves. It also addresses the problem of the efficient evaluation of pairings over Huff ...
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Diophantine $m$-tuples and elliptic curves
... Diophantine m-tuples and elliptic curves par ANDREJ DUJELLA RESUME. Un m-uplet diophantien est un ensemble de m entiers naturels non nuls tel que le produit quelconque de deux d’entre eux augment6 de 1 est un ...
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Visualisation of implicit algebraic curves
... The first type is inspired by the Cylindrical Alge- braic Decomposition [5] algorithm. They use projec- tion techniques based on a conceptual sweeping line perpendicular to some axis that detects the critical topological ...
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Monotonicity Analysis over Chains and Curves
... 2007 Curves Dan Kucerovsky and Daniel Lemire ...chains curves by generalizing the scalar-valued con- cept of ...Monotone curves may be discontinuous, but continuous monotone curves are ...
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Fundamental domains for Shimura curves
... elliptic points to serve as base vertices for a fundamental domain. The background material for this work follows closely the comprehensive book of Vignéras [13], to which we refer the reader for further information. In ...
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On equations defining fake elliptic curves
... 3. Algebraic models for genus 2 curves Now suppose that we are given a point Z ∈ H 2 and consider the torus J Z attached to it. Given a pair (c 1 , c 2 ) of different odd characteristics and the corresponding pair ...
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Modelling systems defined by RTD curves
... RIO curves are used for modelling these premises with an application in the nuclear industry for predicting the airbome pollutant transfers in order to prevent radiological ...
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On curves with one place at infinity
... C : F = 0 is the projective closure of C in P 2 K . Furthermore, p = (0, 1, 0) is the unique point at infinity of ¯ C and F (u, 1, y) is the local equation of ¯ C at p. We say that f has one place at infinity if F (u, 1, ...
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Indifferentiable Hashing to Barreto–Naehrig Curves
... elliptic curves BN curves are a family of pairing-friendly elliptic curves over large prime fields, introduced in 2005 by Barreto and Naehrig ...BN curves are of prime order (in particular they ...
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