2024/12/04 by Zhizhong Huang, Huang, Zhizhong
Mathematics · Engineering · #Mathematical Approximation and Integration #Advanced Numerical Methods in Computational Mathematics #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2412.03350
We derive asymptotic formulas with a secondary term for the (smoothly weighted) count of number of integer solutions of height \leqslant B with local conditions to the equation F(x1,x2,x3)=m, where F is a non-degenerate indefinite ternary integral quadratic form, and m is a non-zero integer satisfying -mΔF=\square which can grow like O(B2-θ) for some fixed θ>0. Our approach is based on the δ-variant of the Hardy--Littlewood circle method developed by Heath-Brown.