Results 11 to 20 of about 1,231,297 (284)
Rational points on a certain genus 2 curve
Comptes Rendus. Mathématique, 2023 We give a correct proof to the fact that all rational points on the curve \[ y^2=(x^2+1)(x^2+3)(x^2+7) \] are $\pm \infty $ and $(\pm 1,\,\pm 8)$. This corrects previous works of Cohen [3] and Duquesne [4, 5].
Nguyen, Xuan Tho
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Rational points on quartics [PDF]
Duke Mathematical Journal, 2000 32 pages ...
Harris, Joe, Tschinkel, Yuri
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On rational points in CFT moduli spaces
Journal of High Energy Physics, 2021 Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there.
Nathan Benjamin +3 more
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Rational Singularities and Rational Points [PDF]
Pure and Applied Mathematics Quarterly, 2008 Comment: 12 ...
Blickle, Manuel, Esnault, Hélène
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Families of polynomials of every degree with no rational preperiodic points
Comptes Rendus. Mathématique, 2021 Let $K$ be a number field. Given a polynomial $f(x)\in K[x]$ of degree $d\ge 2$, it is conjectured that the number of preperiodic points of $f$ is bounded by a uniform bound that depends only on $d$ and $[K:\mathbb{Q}]$.
Sadek, Mohammad
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Heights on stacks and a generalized Batyrev–Manin–Malle conjecture
Forum of Mathematics, Sigma, 2023 We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties.
Jordan S. Ellenberg +2 more
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Density of rational points on isotrivial rational elliptic surfaces [PDF]
, 2011 For a large class of isotrivial rational elliptic surfaces (with section), we show that the set of rational points is dense for the Zariski topology, by carefully studying variations of root numbers among the fibers of these surfaces.
Anthony Várilly-Alvarado +14 more
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Game interrupted: The rationality of considering the future [PDF]
Judgment and Decision Making, 2013 The ``problem of points'', introduced by Paccioli in 1494 and solved by Pascal and Fermat 160 years later, inspired the modern concept of probability. Incidentally, the problem also shows that rational decision-making requires the consideration of future
Brandon Almy, Joachim I. Krueger
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Varieties with too many rational points [PDF]
, 2016 We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.Comment: 23 ...
Browning, T. D., Loughran, D.
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Counting rational points on quadric surfaces
Discrete Analysis, 2018 Counting rational points on quadric surfaces, Discrete Analysis 2018:15, 29 pp. A _quadric hypersurface_ of dimension $D$ is the zero set of a quadratic form $Q$ in $D+2$ variables. If $Q(x_1,\dots,x_{D+2})=0$, then $Q(\lambda x_1,\dots,\lambda x_{D+2})=
Tim Browning, Roger Heath-Brown
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