Inhomogeneous quadratic congruences
S. Baier, T.D. Browning
TL;DR
This paper studies the distribution of integer solutions to specific inhomogeneous quadratic congruences and applies these findings to identify almost prime points on a particular algebraic surface.
Contribution
It introduces new methods for analyzing inhomogeneous quadratic congruences and applies them to problems in algebraic geometry involving del Pezzo surfaces.
Findings
Density estimates for solutions to quadratic congruences
Detection of almost primes on a degree 6 del Pezzo surface
New techniques for inhomogeneous quadratic analysis
Abstract
We investigate the density of integer solutions to certain binary inhomogeneous quadratic congruences and use this information to detect almost primes on a singular del Pezzo surface of degree 6.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Mathematical Identities