Results 1 to 10 of about 1,551 (43)
Diophantine non-integrability of a third order recurrence with the Laurent property [PDF]
, 2006 We consider a one-parameter family of third order nonlinear recurrence relations. Each member of this family satisfies the singularity confinement test, has a conserved quantity, and moreover has the Laurent property: all of the iterates are Laurent ...
Hone, Andrew N.W.
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Heights and quadratic forms: on Cassels' theorem and its generalizations [PDF]
, 2012 In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally ...
Fukshansky, Lenny
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A Kolmogorov theorem for nearly-integrable Poisson systems with asymptotically decaying time-dependent perturbation [PDF]
, 2014 The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly-integrable Poisson systems associated to a real analytic Hamiltonian with aperiodic time dependence, provided that the perturbation is asymptotically ...
A Fortunati +11 more
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Superconformal Block Quivers, Duality Trees and Diophantine Equations [PDF]
, 2013 We generalize previous results on N = 1, (3 + 1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, i.e.
A Hanany +38 more
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On the algebraic structure of rational discrete dynamical systems [PDF]
, 2015 We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy as ...
Viallet, Claude M.
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Bounds for eigenforms on arithmetic hyperbolic 3-manifolds [PDF]
, 2015 On a family of arithmetic hyperbolic 3-manifolds of squarefree level, we prove an upper bound for the sup-norm of Hecke-Maass cusp forms, with a power saving over the local geometric bound simultaneously in the Laplacian eigenvalue and the volume.
Blomer, Valentin +2 more
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Elliptic Curves and Hyperdeterminants in Quantum Gravity [PDF]
, 2010 Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely ignored over a period of 100 years before once again being recognised as ...
Gibbs, Philip
core
Explicit Chabauty-Kim theory for the thrice punctured line in depth two
, 2014 Let $X= \mathbb{P}^1 \setminus \{0,1,\infty\}$, and let $S$ denote a finite set of prime numbers. In an article of 2005, Minhyong Kim gave a new proof of Siegel's theorem for $X$: the set $X(\mathbb{Z}[S^{-1}])$ of $S$-integral points of $X$ is finite ...
Beı˘linson +26 more
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Laurent Polynomials and Superintegrable Maps [PDF]
, 2007 This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 ...
Hone, Andrew N.W.
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Rational analogs of projective planes
, 2014 In this paper, we study the existence of high-dimensional, closed, smooth manifolds whose rational homotopy type resembles that of a projective plane. Applying rational surgery, the problem can be reduced to finding possible Pontryagin numbers satisfying
Su, Zhixu
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