Results 11 to 20 of about 3,799,599 (344)
Rational and singular points of a family of curves
Results in Applied MathematicsThis paper explores the properties of a family of absolutely irreducible projective plane curves, denoted Ca,b, which are defined over a finite field Fm of characteristic 2.
M.C. Rodríguez-Palánquex
doaj +2 more sources
Some aspects of rational points and rational curves
, 2023 Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context (rational points over number fields) and in an algebro-geometric one (rational curves on real varieties), and discuss
Wittenberg, Olivier
openaire +4 more sources
Expositiones mathematicae, 2023 We compute the rational points on the Atkin–Lehner quotient X0+(125) using the quadratic Chabauty method. Our work completes the study of exceptional rational points on the curves X0+(N) of genus between 2 and 6. Together with the work of several authors,
V. Arul, J. Müller
semanticscholar +2 more sources
Counting rational points of a Grassmannian
Monatshefte für Mathematik, 2022 We prove an estimate on the number of rational points on the Grassmannian variety of bounded twisted height, refining the classical results of Schmidt ([12]) and Thunder ([20]) over the rational field: most importantly, our formula counts all points. Among the consequences are a couple of new implications on the classical subject of counting rational ...
Kim, Seungki
openaire +4 more sources
Rational points on curves [PDF]
Journal de théorie des nombres de Bordeaux, 2011 This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009. We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve C
Michael Stoll, Stoll, Michael
openaire +4 more sources
A conjecture on rational approximations to rational points
Journal of Algebraic Geometry, 2006 In this paper, we examine how well a rational point P P on an algebraic variety
David McKinnon
openaire +3 more sources
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
Rational points on quartics [PDF]
Duke Mathematical Journal, 2000 32 pages ...
Harris, Joe, Tschinkel, Yuri
openaire +4 more sources
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
, 2021 In this paper we develop an explicit method for studying the distribution of rational points near manifolds. As a consequence we obtain optimal lower bounds on the number of rational points of bounded height lying at a given distance from an arbitrary ...
V. Beresnevich +3 more
semanticscholar +1 more source