Results 1  10
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84
Mahler's Measure and Special Values of Lfunctions
, 1998
"... this paper is to describe an attempt to understand and generalize a recent formula of Deninger [1997] by means of systematic numerical experiment. This conjectural formula, ..."
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Cited by 64 (1 self)
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this paper is to describe an attempt to understand and generalize a recent formula of Deninger [1997] by means of systematic numerical experiment. This conjectural formula,
Hessian Elliptic Curves and SideChannel Attacks
 of Lecture Notes in Computer Science
, 2001
"... Sidechannel attacks are a recent class of attacks that have been revealed to be very powerful in practice. By measuring some sidechannel information (running time, power consumption, . . . ), an attacker is able to recover some secret data from a carelessly implemented cryptoalgorithm. ..."
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Cited by 49 (7 self)
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Sidechannel attacks are a recent class of attacks that have been revealed to be very powerful in practice. By measuring some sidechannel information (running time, power consumption, . . . ), an attacker is able to recover some secret data from a carelessly implemented cryptoalgorithm.
Topological strings and (almost) modular forms
, 2007
"... The Bmodel topological string theory on a CalabiYau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H 3 (X). We show that, depending on the cho ..."
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Cited by 47 (6 self)
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The Bmodel topological string theory on a CalabiYau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H 3 (X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasimodular form or an almost holomorphic modular form of weight 0 under Γ. Moreover, at each genus, certain combinations of genus g amplitudes are both modular and holomorphic. We illustrate this for the local CalabiYau manifolds giving rise to SeibergWitten gauge theories in four dimensions and local IP2 and IP1×IP1. As a byproduct, we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space, which we use to give predictions for GromovWitten invariants of the orbifold C 3 / Z3.
Constructing Isogenies Between Elliptic Curves Over Finite Fields
 LMS J. Comput. Math
, 1999
"... Let E 1 and E 2 be ordinary elliptic curves over a finite field Fp such that #E1 (Fp ) = #E2 (Fp ). Tate's isogeny theorem states that there is an isogeny from E1 to E2 which is defined over Fp . The goal of this paper is to describe a probabilistic algorithm for constructing such an isogeny. ..."
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Cited by 29 (3 self)
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Let E 1 and E 2 be ordinary elliptic curves over a finite field Fp such that #E1 (Fp ) = #E2 (Fp ). Tate's isogeny theorem states that there is an isogeny from E1 to E2 which is defined over Fp . The goal of this paper is to describe a probabilistic algorithm for constructing such an isogeny.
Explicit 4descents on an elliptic curve
 Acta Arith
, 1996
"... Abstract. It is shown that the obvious method of descending from an element of the 2Selmer group of an elliptic curve, E, will indeed give elements of order 1, 2 or 4 in the WeilChatelet group of E. Explicit algorithms for such a method are given. 1. ..."
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Cited by 20 (3 self)
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Abstract. It is shown that the obvious method of descending from an element of the 2Selmer group of an elliptic curve, E, will indeed give elements of order 1, 2 or 4 in the WeilChatelet group of E. Explicit algorithms for such a method are given. 1.
Efficient Solution of Rational Conics
 Math. Comp
, 1998
"... this paper (section 2), and to Denis Simon for the reference [10]. ..."
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Cited by 19 (0 self)
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this paper (section 2), and to Denis Simon for the reference [10].
Primes Generated by Elliptic Curves
, 2003
"... For a rational elliptic curve in Weierstrass form, Chudnovsky and Chudnovsky considered the likelihood that the denominators of the xcoordinates of the multiples of a rational point are squares of primes. Assuming the point is the image of a rational point under an isogeny, we use Siegel’s Theorem t ..."
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Cited by 19 (9 self)
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For a rational elliptic curve in Weierstrass form, Chudnovsky and Chudnovsky considered the likelihood that the denominators of the xcoordinates of the multiples of a rational point are squares of primes. Assuming the point is the image of a rational point under an isogeny, we use Siegel’s Theorem to prove that only finitely many primes will arise. The same question is considered for elliptic curves in homogeneous form, prompting a visit to Ramanujan’s famous taxicab equation. Finiteness is provable for these curves with no extra assumptions. Finally, consideration is given to the possibilities for prime generation in higher rank.
SYMPLECTIC AUTOMORPHISMS OF PRIME ORDER ON K3 SURFACES
, 2008
"... Abstract. We study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients (by a result of Nikulin this action is independent on the choice ..."
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Cited by 13 (8 self)
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Abstract. We study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients (by a result of Nikulin this action is independent on the choice of the K3 surface). With the help of elliptic fibrations we determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the CoxeterTodd lattice in the case of automorphism of order three. In the paper [Ni1] Nikulin studies finite abelian groups G acting symplectically (i.e. G H2,0(X,C) = id H2,0(X,C)) on K3 surfaces (defined over C). One of his main result is that the action induced by G on the cohomology group H2 (X, Z) is unique up to isometry. In [Ni1] all abelian finite groups of automorphisms of a K3 surface acting symplectically
Functional equations for Mahler measures of genusone curves
 ALGEBRA AND NUMBER THEORY
"... In this paper we will establish functional equations for Mahler measures of families of genusone twovariable polynomials. These families were previously studied by Beauville [3], and their Mahler measures were considered by Boyd [11] and RodriguezVillegas [19]. Bertin [8], Zagier [26], and Stiens ..."
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Cited by 13 (11 self)
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In this paper we will establish functional equations for Mahler measures of families of genusone twovariable polynomials. These families were previously studied by Beauville [3], and their Mahler measures were considered by Boyd [11] and RodriguezVillegas [19]. Bertin [8], Zagier [26], and Stienstra [24]. Our functional equations allow us to prove identities between Mahler measures that were conjectured by Boyd. As a corollary, we also establish some new transformations for hypergeometric functions.
Explicit equations of some elliptic modular surfaces
 J. OF MATH
, 2007
"... We present explicit equations of semistable elliptic surfaces (i.e., having only type In singular fibers) which are associated to the torsionfree genus zero congruence subgroups of the modular group as classified by A. Sebbar. ..."
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Cited by 12 (1 self)
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We present explicit equations of semistable elliptic surfaces (i.e., having only type In singular fibers) which are associated to the torsionfree genus zero congruence subgroups of the modular group as classified by A. Sebbar.