• Corpus ID: 117607432

Groupe de Brauer et points entiers de deux surfaces cubiques affines

  title={Groupe de Brauer et points entiers de deux surfaces cubiques affines},
  author={Jean-Louis Colliot-Th{\'e}l{\`e}ne and Olivier Wittenberg},
Il est connu depuis Ryley [Ryl25] que tout entier, et meme tout nombre rationnel, peut s’ecrire comme somme de trois cubes de nombres rationnels. La question de savoir quels entiers s’ecrivent comme sommes de trois cubes d’entiers relatifs, en revanche, est toujours ouverte. Un tel entier ne peut etre congru a 4 ou 5 modulo 9. Plusieurs auteurs ont conjecture que reciproquement, tout entier non congru a 4 ou 5 modulo 9 est la somme de trois cubes d’entiers relatifs (cf. [HB92, p. 623], [CV94… 
1 Citations
Nauseating Notation Very Much in Draft
1 the abuses of language without which any mathematical text threatens to become pedantic and even unreadable. [3] but some abuse is more harmful than others. 1 Intervals We raise this old chestnut


Brauer–Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms
Abstract An integer may be represented by a quadratic form over each ring of p-adic integers and over the reals without being represented by this quadratic form over the integers. More generally,
Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties.
Classes of varieties satisfying this principle are known other than quadrics (e.g. SeveriBrauer varieties and more generally complete varieties which are homogeneous spaces under a connected linear
over the ring of integers Z, where A and B are non-degenerate and symmetric matrices of size m × m and n × n over Z respectively, and A is indefinite with m ≥ 3. It is a necessary condition for
A Note on the Diophantine Equation x 3 + y 3 + z 3 = 3
Any integral solution of the title equation has x =y z (9). The report of Scarowsky and Boyarsky [3] that an extensive computer search has failed to turn up any further integral solutions of the
Sums of cubes in polynomial rings
For any associative ring A with 1 of prime characteristic ^0, 2, 3 , every element of A is the sum of three cubes in A . For any ring A, let w}(A) denote the least integer s > 0 such that every sum
The density of zeros of forms for which weak approximation fails
The weak approximation principal fails for the forms x + y + z = kw, when k = 2 or 3. The question therefore arises as to what asymptotic density one should predict for the rational zeros of these
On searching for solutions of the Diophantine equation x3 + y3 +2z3 = n
An efficient search algorithm to solve the equation x3 + y3 + 2z3 = n for a fixed value of n > 0 by parametrizing |z| and obtains |x| and |y| (if they exist) by solving a quadratic equation derived from divisors of 2|z|3±n.
Two examples of Brauer–Manin obstruction to integral points
We give two examples of Brauer-Manin obstructions to integral points on open subsets of the projective plane.
Jahnel -« New sums of three cubes
  • Math. Comp
  • 2009
Wright -An introduction to the theory of numbers, sixième éd
  • 2008