Bihomogeneous forms in many variables
Journal de Théorie des Nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 483-506.

We count integer points on varieties given by bihomogeneous equations using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in using the standard approach for homogeneous varieties. Also, we consider counting functions where not all the variables have to lie in intervals of the same size, which arises as a natural question in the setting of bihomogeneous varieties.

Nous comptons les points entiers sur des variétés données par des équations bihomogènes en utilisant la méthode de Hardy–Littlewood. La principale nouveauté est l’utilisation de la structure des équations bihomogènes pour obtenir, de manière générique, des estimations asymptotiques pour moins de variables que ne le permette l’approche classique pour les variétés homogènes. Nous considérons aussi des fonctions de comptage où toutes les variables n’appartiennent pas nécessairement à des intervalles de même taille, ce qui se présente comme une question naturelle dans le cadre des variétés bihomogènes.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.876
Classification: 11D45,  11D72,  11P55
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Damaris Schindler. Bihomogeneous forms in many variables. Journal de Théorie des Nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 483-506. doi : 10.5802/jtnb.876. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.876/

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