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In [[mathematics]], the '''Landau–Ramanujan constant''' occurs in a [[number theory]] result stating that the number of [[positive integer]]s less than ''x'' that are the sum of two [[square number]]s, for large ''x'', [[proportionality (mathematics)|varies as]]


:<math>x/{\sqrt{\ln(x)}}.</math>


The [[mathematical constant|constant]] of proportionality is the Landau–Ramanujan constant, which was discovered independently by [[Edmund Landau]] and [[Srinivasa Ramanujan]].
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More formally, if ''N''(''x'') is the number of positive integers less than ''x'' which are the sum of two squares, then
:<math>\lim_{x\rightarrow\infty} \frac{N(x)\sqrt{\ln(x)}}{x}\approx 0.76422365358922066299069873125.</math>
 
== External links ==
* {{MathWorld|urlname=Landau-RamanujanConstant|title=Landau–Ramanujan Constant}}
* {{OEIS|A064533}}
 
{{DEFAULTSORT:Landau-Ramanujan constant}}
[[Category:Additive number theory]]
[[Category:Analytic number theory]]
[[Category:Mathematical constants]]
[[Category:Srinivasa Ramanujan]]
 
 
{{Numtheory-stub}}

Revision as of 05:11, 6 February 2014


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