Results 1 to 10 of about 1,231,297 (284)
Lattices and Rational Points [PDF]
Mathematics, 2017 In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N - 1 on transverse curves in E N , where E is an elliptic curve without Complex
Evelina Viada
doaj +4 more sources
Primitive points in rational polygons [PDF]
Canadian Mathematical Bulletin, 2019 Let $\mathcal A$ 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 $\frac6{\pi^2}$ Area$(t\mathcal A)$ as $t\to \infty$. We show that
Bárány, Imre +3 more
core +5 more sources
Sieving rational points on varieties [PDF]
Transactions of the American Mathematical Society, 2018 A sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, the number of varieties in a family which are everywhere locally soluble, and to the notion of friable rational points ...
Browning, Tim, Loughran, Daniel
core +8 more sources
Rational points on X_0^+ (p^r)
, 2011 We show how the recent isogeny bounds due to \'E. Gaudron and G. R\'emond allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime exceeding 2.10^{11}. This includes the case of the curves X_split (p).
Bilu, Yu., Parent, P., Rebolledo, M.
core +5 more sources
Quartic surfaces, their bitangents and rational points [PDF]
Épijournal de Géométrie Algébrique, 2023 Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K.
Pietro Corvaja, Francesco Zucconi
doaj +1 more source
Which rational double points occur on del Pezzo surfaces? [PDF]
Épijournal de Géométrie Algébrique, 2021 We determine all configurations of rational double points that occur on RDP del Pezzo surfaces of arbitrary degree and Picard rank over an algebraically closed field $k$ of arbitrary characteristic ${\rm char}(k)=p \geq 0$, generalizing classical work of
Claudia Stadlmayr
doaj +1 more source
On homogeneous spaces with finite anti-solvable stabilizers
Comptes Rendus. Mathématique, 2022 We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for $n\ne 6$ and all 26 sporadic simple groups. We prove that,
Lucchini Arteche, Giancarlo
doaj +1 more source
Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve
Journal of Mathematical Sciences and Modelling, 2021 In this paper, we give a parametrization of algebraic points of degree at most $4$ over $\mathbb{Q}$ on the schaeffer curve $\mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr.
Moussa Fall
doaj +1 more source
New sequences of non-free rational points
Comptes Rendus. Mathématique, 2021 We exhibit some new infinite families of rational values of $\tau $, some of them squares of rationals, for which the group or even the semigroup generated by the matrices $({{\textstyle \begin{matrix} 1 & 1\\ 0 & 1 \end{matrix}}})$ and $({{\textstyle ...
Smilga, Ilia
doaj +1 more source
Quartic and Quintic Hypersurfaces with Dense Rational Points
Forum of Mathematics, Sigma, 2023 Let $X_4\subset \mathbb {P}^{n+1}$ be a quartic hypersurface of dimension $n\geq 4$ over an infinite field k. We show that if either $X_4$ contains a linear subspace $\Lambda $ of dimension $h\geq \max \{2,\dim (\Lambda ...
Alex Massarenti
doaj +1 more source