Distribution of integer points on determinant surfaces and a mod‐ p analogue

Key Points

• The goal is to count integer solutions to specific equations and congruences, assessing their error terms.
• Developed asymptotic formulas for integer solutions with smooth weights.
• Analyzed integer solutions related to determinant surfaces.
• Considered congruences involving large primes.
• Established an explicit main term for integer solution counts.
• Provided strong bounds on the error term based on variable sizes.
• Counted integer solutions effectively in both determinant equations and congruences.

Abstract