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| {{primary sources|date=August 2012}}
| | Hi there. My name is Sophia Meagher even though it is not the name on my birth certificate. My day job is a travel agent. I am really fond of to go to karaoke but I've been taking on new issues recently. Mississippi is where her home is but her spouse wants them to transfer.<br><br>Feel free to surf to my weblog good psychic ([http://netwk.hannam.ac.kr/xe/data_2/85669 netwk.hannam.ac.kr]) |
| The '''Heath-Brown–Moroz''' constant ''C'',<ref>{{cite journal|author=D. R. Heath-Brown | authorlink=Roger Heath-Brown | coauthors=B.Z. Moroz | title=The density of rational points on the cubic surface ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1</sub>''X''<sub>2</sub>''X''<sub>3</sub> | journal=Mathematical Proceedings of the Cambridge Philosophical Society | volume=125 | pages=385–395 | year=1999|doi=10.1017/S0305004198003089 | issue=3}}</ref> named for [[Roger Heath-Brown]] and [[Boris Moroz]], is defined as
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| :<math>C=\prod_p\left(1-\frac{1}{p}\right)^7\left(1+\frac{7p+1}{p^2}\right) = 0.001317641... </math>
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| where ''p'' runs over the [[Prime number|primes]]. | |
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| This constant is part of an [[asymptotic estimate]] for the distribution of [[rational point]]s of bounded [[height function|height]] on the [[cubic surface]] ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1</sub>''X''<sub>2</sub>''X''<sub>3</sub>. Let ''H'' be a positive real number and ''N''(''H'') the number of solutions to the equation ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1</sub>''X''<sub>2</sub>''X''<sub>3</sub> with all the ''X''<sub>''i''</sub> non-negative integers less than or equal to ''H'' and their [[greatest common divisor]] equal to 1. Then
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| :<math>N(H)= C \cdot \frac{H(\log H)^6} {4\times 6!} + O(H(\log H)^5).</math>
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| ==References==
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| <references/>
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| {{DEFAULTSORT:Heath-Brown-Moroz constant}}
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| [[Category:Mathematical constants]]
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| {{numtheory-stub}}
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| {{num-stub}}
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Latest revision as of 23:37, 5 January 2015
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