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.[1][2]

Application

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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 Xi non-negative integers less than or equal to H and their greatest common divisor equal to 1. Then

 .

References

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  1. ^ D. R. Heath-Brown; B.Z. Moroz (1999). "The density of rational points on the cubic surface X03=X1X2X3". Mathematical Proceedings of the Cambridge Philosophical Society. 125 (3): 385–395. Bibcode:1999MPCPS.125..385H. doi:10.1017/S0305004198003089. S2CID 59947536.
  2. ^ Finch, S. R (2003). Mathematical Constants. Cambridge, England: Cambridge University Press.
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