# 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 $z\le N$ 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

$$\underset{N\to \mathrm{\infty}}{lim}\frac{L(N)\sqrt{\mathrm{log}(N)}}{N}\approx 0.76422365358922066299069873125$$ |

Title | Landau-Ramanujan Constant |
---|---|

Canonical name | LandauRamanujanConstant |

Date of creation | 2014-03-06 12:39:16 |

Last modified on | 2014-03-06 12:39:16 |

Owner | Filipe (28191) |

Last modified by | Filipe (28191) |

Numerical id | 2 |

Author | Filipe (28191) |

Entry type | Definition |