منابع مشابه
A Note on the Rational Points
Let C be the image of a canonical embedding φ of the Atkin-Lehner quotient X + 0 (N) associated to the Fricke involution w N. Suppose φ is defined over the rationals. In this note we give some collinearity relations among rational points of C, for each X + 0 (N) of genus 3 and the first X + 0 (N) of genus 4, for N prime.
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Let C be the image of a canonical embedding φ of the Atkin-Lehner quotient X 0 (N) associated to the Fricke involution wN . In this note we exhibit some relations among the rational points of C. For each g = 3 (resp. the first g = 4) curve C we found that there are one or more lines (resp. planes) in P whose intersection with C consists entirely of rational Heegner points or the cusp point, whe...
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The problem to decide whether a given algebraic variety defined over the rational numbers has rational points is fundamental in Arithmetic Geometry. Abstracting from concrete examples, this leads to the question whether there exists an algorithm that is able to perform this task for any given variety. This is probably too much to ask for: we know that Hilbert’s Tenth Problem, which asks the sam...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1958
ISSN: 0386-2194
DOI: 10.3792/pja/1195524674