## An introduction to the analytic theory of numbers |

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### Contents

Distribution of primes | 37 |

The theory of partitions | 135 |

Warings problem | 206 |

Copyright | |

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### Common terms and phrases

abscissa of convergence absolutely convergent analytic argument asymptotic formula bounded Cauchy's theorem Chapter character mod character modulo choose class number coefficients completes the proof congruence Consequently consider converges absolutely corollary deduce defined Dirichlet series discriminant equivalent estimate Euler-MacLaurin formula Euler's evaluate exist infinitely exists a constant fact factor Farey Farey series finite hand hence inequality infer infinitely many primes inner sum integer integral integrand interval Kronecker symbol lattice points Lemma log C(s log log major arcs Math minor arc modular modulo Moreover multiplicative number of partitions number of solutions prime ideal prime number theorem problem proof of Theorem properties prove Theorem quadratic field real number relation residue classes residue system result Riemann hypothesis right-hand side root of unity second sum simple pole solvable summation Suppose term Theorem 3.1 transformation Vinogradoff zeta function