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Heath-Brown–Moroz constant
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Heath-Brown–Moroz constant : ウィキペディア英語版
Heath-Brown–Moroz constant

The Heath-Brown–Moroz constant ''C'', named for Roger Heath-Brown and Boris Moroz, is defined as
:C=\prod_p\left(1-\frac\right)^7\left(1+\frac\right) = 0.001317641...
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 ''X''03=''X''1''X''2''X''3. Let ''H'' be a positive real number and ''N''(''H'') the number of solutions to the equation ''X''03=''X''1''X''2''X''3 with all the ''X''''i'' non-negative integers less than or equal to ''H'' and their greatest common divisor equal to 1. Then
:N(H)= C \cdot \frac + O(H(\log H)^5).
==References==



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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