Counting solutions to quadratic polynomials

TL;DR

This paper employs the circle method to derive uniform asymptotic formulas for counting integer solutions to specific quadratic polynomials, advancing understanding of their solution distribution.

Contribution

It introduces a new approach that provides uniform asymptotic estimates for solutions across various quadratic polynomials.

Findings

Derived asymptotic formulas for solution counts

Achieved uniformity in coefficients

Enhanced understanding of quadratic polynomial solutions

Abstract

Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.