## Elementary methods in the analytic theory of numbers |

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34 pages matching **CHAPTER** in this book

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### Contents

An Elementary Solution of Warinos Problem | 13 |

The Problem of the Distribution of Primes | 42 |

An Elementary Derivation of the Law of Distri | 77 |

Copyright | |

11 other sections not shown

### Common terms and phrases

2Nlln apply Lemma arithmetic progression asymptotic formula basis CHAPTER character modulo coefficients congruence Consequently consider the sum constant contour corresponding curve defined denote distribution of primes divides exactly elementary methods elementary proof equal equation Euler's function exceed exists function fundamental lemma Further Gaussian integers Gaussian primes Hence integral-valued vectors interval irreducible left-hand side Liouville function Mobius function n<x n non-principal character number of integral number of numbers number of primes number of solutions obtain obviously polynomial positive integers properties quadratic forms quadratic nonresidue quadratic residue real numbers relatively prime remainder term Riemann hypothesis right-hand side rk(m Rolle's Theorem satisfying the conditions Schnirelmann's Schnirelmann's Theorem sequence sieve sufficiently large numbers summation system of numbers theory of numbers upper bound values Vinogradov Vinogradov's Theorem virtue Waring's problem whence it follows Xn+1 zeros