Heath-Brown–Moroz constant

The Heath-Brown–Moroz constant C, named for Roger Heath-Brown and Boris Moroz, is defined as

where p runs over the primes.

This constant is part of an asymptotic estimate for the distribution of rational points of bounded height on the cubic surface X₀³=X₁X₂X₃. Let H be a positive real number and N(H) the number of solutions to the equation X₀³=X₁X₂X₃ with all the X_i non-negative integers less than or equal to H and their greatest common divisor equal to 1. Then

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