Let . In this Note, we explain how to determine the asymptotic behaviour of the size of the set of rational points (where and ) of bounded height on the hyperplane such that is squareful for each as B goes to infinity. (An integer a is called squareful if the exponent of each prime divisor of a is at least two.) The main tool we will use, is the (classical) Hardy–Littlewood circle method.
Soit . Dans cette Note, nous expliquerons comment on peut déterminer le comportement asymptotique du nombre de points rationnels (avec et ) de hauteur bornée sur lʼhyperplan tels que est un entier puissant pour chaque , lorsque B tend vers lʼinfini. (Un entier a est appelé puissant si pour chaque nombre premier p divisant a, on a que aussi divise a.) La méthode principale quʼon utilise ici est la méthode du cercle de Hardy–Littlewood (classique).
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Karl Van Valckenborgh 1
@article{CRMATH_2011__349_11-12_603_0, author = {Karl Van Valckenborgh}, title = {Squareful points of bounded height}, journal = {Comptes Rendus. Math\'ematique}, pages = {603--606}, publisher = {Elsevier}, volume = {349}, number = {11-12}, year = {2011}, doi = {10.1016/j.crma.2011.05.001}, language = {en}, }
Karl Van Valckenborgh. Squareful points of bounded height. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 603-606. doi : 10.1016/j.crma.2011.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.001/
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