In his paper from 1996 on quadratic forms Heath-Brown developed a version of the circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight, and approximated this quantity by the integral of the weight function against a measure on the quadric. The weight function is assumed to be C∞₀-smooth and vanish near the singularity of the quadric. In our work we allow the weight function to be finitely smooth, not vanish at the singularity and have an explicit decay at infinity. The paper uses only elementary number theory and is available to readers without a number-theoretical background.

Vladut, S., Dymov, A., Kuksin, S., Maiocchi, A. (2023). Уточнение теоремы Хис-Брауна о квадратичных формах. SBORNIK MATHEMATICS, 214(5), 18-68 [10.4213/sm9711].

Уточнение теоремы Хис-Брауна о квадратичных формах

A, Maiocchi
2023

Abstract

In his paper from 1996 on quadratic forms Heath-Brown developed a version of the circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight, and approximated this quantity by the integral of the weight function against a measure on the quadric. The weight function is assumed to be C∞₀-smooth and vanish near the singularity of the quadric. In our work we allow the weight function to be finitely smooth, not vanish at the singularity and have an explicit decay at infinity. The paper uses only elementary number theory and is available to readers without a number-theoretical background.
Articolo in rivista - Articolo scientifico
Quadratic forms, circle method
Russian
2023
214
5
18
68
open
Vladut, S., Dymov, A., Kuksin, S., Maiocchi, A. (2023). Уточнение теоремы Хис-Брауна о квадратичных формах. SBORNIK MATHEMATICS, 214(5), 18-68 [10.4213/sm9711].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/425938
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