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Bihomogeneous forms in many variables. (English. French summary) Zbl 1425.11055

Summary: 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.

MSC:

11D45 Counting solutions of Diophantine equations
11D72 Diophantine equations in many variables
11P55 Applications of the Hardy-Littlewood method
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References:

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