Landau-Ramanujan Constant

Let $N$ be a natural number. Consider the equation

x^{2}+y^{2}=N

Let $L(N)$ denote the number of naturals $z\\leq N$ such that the equation $x^{2}+y^{2}=z$ has at least one integer solution $(x,y)$ .The Laudau-Ramanujan constant is defined as the limit

\\lim_{N\\rightarrow\\infty}\\frac{L(N)\\sqrt{\\log(N)}}{N}\\approx 0.764223653589220%66299069873125

随便看

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