Results 31 to 40 of about 3,799,599 (344)
The density of rational points near hypersurfaces [PDF]
, 2017 We establish a sharp asymptotic formula for the number of rational points up to a given height and within a given distance from a hypersurface. Our main innovation is a bootstrap method that relies on the synthesis of Poisson summation, projective ...
Jing-Jing Huang
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Counting rational points on biquadratic hypersurfaces [PDF]
Advances in Mathematics, 2018 An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski open subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables.
T. Browning, L. Hu
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Rational points of quiver moduli spaces [PDF]
Annales de l'Institut Fourier, 2017 For a perfect field $k$, we study actions of the absolute Galois group of $k$ on the $\overline{k}$-valued points of moduli spaces of quiver representations over $k$; the fixed locus is the set of $k$-rational points and we obtain a decomposition of this
Victoria Hoskins, Florent Schaffhauser
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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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Primitive Points in Rational Polygons [PDF]
Canadian Mathematical Bulletin, 2020 AbstractLet ${\mathcal{A}}$ be a star-shaped polygon in the plane, with rational vertices, containing the origin. The number of primitive lattice points in the dilate $t{\mathcal{A}}$ is asymptotically $\frac{6}{\unicode[STIX]{x1D70B}^{2}}\text{Area}(t{\mathcal{A}})$ as $t\rightarrow \infty$. We show that the error term is both $\unicode[STIX]{x1D6FA}_{
Bárány, I +3 more
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Density of rational points on a quadric bundle in P 3 × P 3 [PDF]
, 2018 An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface $x_1y_1^2+\dots+x_4y_4^2=0$ in $\mathbb{P}^3\times\mathbb{P}^3$.
T. Browning, D. R. Heath-Brown
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Rational Points on Solvable Curves over ℚ via Non-Abelian Chabauty [PDF]
International mathematics research notices, 2017 We study the Selmer varieties of smooth projective curves of genus at least two defined over $\mathbb{Q}$ which geometrically dominate a curve with CM Jacobian. We extend a result of Coates and Kim to show that Kim’s non-abelian Chabauty method applies
J. Ellenberg, D. Hast
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On Rational Points on Conics [PDF]
Proceedings of the American Mathematical Society, 1977 The purpose of this paper is to prove the following result: let K be a finitely, separably generated extension field of transcendence degree one and genus zero over the exact constant field k .
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On the density of rational points on rational elliptic surfaces [PDF]
Acta Arithmetica, 2017 Let $\mathscr{E}\rightarrow\mathbb{P}^1_\mathbb{Q}$ be a non-trivial rational elliptic surface over $\mathbb{Q}$ with base $\mathbb{P}^1_\mathbb{Q}$ (with a section). We conjecture that any non-trivial elliptic surface has a Zariski-dense set of $\mathbb{
J. Desjardins
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Second descent and rational points on Kummer varieties [PDF]
Proceedings of the London Mathematical Society, 2017 A powerful method, pioneered by Swinnerton‐Dyer, allows one to study rational points on pencils of curves of genus 1 by combining the fibration method with a sophisticated form of descent.
Yonatan Harpaz
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