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ELLIPTIC CURVES AND -ADIC ELLIPTIC TRANSCENDENCE
Bulletin of the Australian Mathematical Society, 2021AbstractWe prove a necessary and sufficient condition for isogenous elliptic curves based on the algebraic dependence ofp-adic elliptic functions. As a consequence, we give a short proof of thep-adic analogue of Schneider’s theorem on the linear independence ofp-adic elliptic logarithms of algebraic points on two nonisogenous elliptic curves defined ...
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Handbook of Finite Fields, 2019
A plane curve is the set of the form {(x, y) : f(x, y) = 0} where f(x, y) is a polynomial in two variables. There are many familiar examples of plane curves: for example, the circle (x−3)+(y−2) = 4 is a plane curve, as one sees by taking f(x, y) to be (x−
Joseph H. Silverman
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A plane curve is the set of the form {(x, y) : f(x, y) = 0} where f(x, y) is a polynomial in two variables. There are many familiar examples of plane curves: for example, the circle (x−3)+(y−2) = 4 is a plane curve, as one sees by taking f(x, y) to be (x−
Joseph H. Silverman
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Theory of Probability & Its Applications, 1986
Let \(E_ n=(\xi_{pl})^ n_{p,l=1}\) denote random complex (n\(\times n)\)-matrices. Random vectors \((\xi^ n_{pl},\xi^ n_{lp})\), \(p\geq l\), \(p,l=\overline{s,n}\) are independent, \(M\xi^ n_{pl}=0\), \(M| \xi^ n_{pl}|^ 2=n^{-1}\), \(M\xi^ n_{pl}\xi^ n_{lp}=n^{-1}\rho\), \(l\neq p\), random variables Re \(\xi\) \({}^ n_{pl}\), Im \(\xi\) \({}^ n_{pl}\)
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Let \(E_ n=(\xi_{pl})^ n_{p,l=1}\) denote random complex (n\(\times n)\)-matrices. Random vectors \((\xi^ n_{pl},\xi^ n_{lp})\), \(p\geq l\), \(p,l=\overline{s,n}\) are independent, \(M\xi^ n_{pl}=0\), \(M| \xi^ n_{pl}|^ 2=n^{-1}\), \(M\xi^ n_{pl}\xi^ n_{lp}=n^{-1}\rho\), \(l\neq p\), random variables Re \(\xi\) \({}^ n_{pl}\), Im \(\xi\) \({}^ n_{pl}\)
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Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
Physics Letters, Section A: General, Atomic and Solid State Physics, 2001Zuntao Fu
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Mathematische Nachrichten, 1999
AbstractIf G is the structure group of a manifold M it is shown how a certain ideal in the character ring of G corresponds to the set of geometric elliptic operators on M. This provides a simple method to construct these operators. For classical structure groups like G = O(n) (Riemannian manifolds), G = SO(n) (oriented Riemannian manifolds), G = U(m ...
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AbstractIf G is the structure group of a manifold M it is shown how a certain ideal in the character ring of G corresponds to the set of geometric elliptic operators on M. This provides a simple method to construct these operators. For classical structure groups like G = O(n) (Riemannian manifolds), G = SO(n) (oriented Riemannian manifolds), G = U(m ...
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Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms
International Conference on the Theory and Application of Cryptology and Information Security, 2017We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition ...
M. Rötteler +3 more
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2012
In this chapter we will construct examples of positive elliptic-elliptic RE, i.e. orbits with two elliptic rotations on the sphere \( {\text{S}}^{ 3} \). The first example is that of a 3-body problem in which 3 bodies of equal masses are at the vertices of an equilateral triangle, which has two rotations of the same frequency.
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In this chapter we will construct examples of positive elliptic-elliptic RE, i.e. orbits with two elliptic rotations on the sphere \( {\text{S}}^{ 3} \). The first example is that of a 3-body problem in which 3 bodies of equal masses are at the vertices of an equilateral triangle, which has two rotations of the same frequency.
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Elliptic and Elliptic-Parabolic Type
1964We consider the linear partial differential equation (II-1.1) $$ Du \equiv Au + au = f\,\,where\,Au \equiv \sum\limits_{i,k = 1}^n {{a_{ik}}{u_{{x_i}{x_k}}} + \sum\limits_{i = 1}^n {{a_i}{u_{{x_i}}}} } $$ (1.1) in the normal domain D of R n and x = (x 1, x 2,... , x n ). Let $$ {a_{ik}}(x),{a_i}(x),a(x),f(x)\,\varepsilon \,{C^0}\,\,in\,\,\
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The State of Elliptic Curve Cryptography
Des. Codes Cryptogr., 2000N. Koblitz, A. Menezes, S. Vanstone
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