Year: 2026
Type: preprint
Abstract: For a non-singular quadratic form $F$ in four variables, we study integer solutions to $F=0$ with an arbitrary weight attached to one of the variables. This allows us to investigate genuinely sparse subsets of the corresponding variety. Our main input is to obtain cancellation in sums of character sums over the moduli arising in the application of the DFI's delta method to the quadratic hypersurface. This cancellation relies crucially on the equidistribution of quadratic roots and the Weil bound for Kloosterman sums.
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221551384