Proves asymptotic count of solutions to x1 x2 - x3 x4 = h for xi in [-N, N] with square-root cancellation when h = N^2 + O(N), confirming a prior speculation.
Meurman,On the binary additive divisor problem, Number theory (Turku, 1999), 223—246, Walter de Gruyter & Co., Berlin
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T(h,N) equals (16/ζ(2)) N² times the sum of 1/d over divisors d of h, plus an error O_ε(N^ε (N + h)).
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Counting solutions to the quadratic determinant equation
Proves asymptotic count of solutions to x1 x2 - x3 x4 = h for xi in [-N, N] with square-root cancellation when h = N^2 + O(N), confirming a prior speculation.
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Counting $2 \times 2$ integer matrices with a given determinant
T(h,N) equals (16/ζ(2)) N² times the sum of 1/d over divisors d of h, plus an error O_ε(N^ε (N + h)).