## Number TheoryThe aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory. The author tries to show the connection between number theory and other branches of mathematics with the resultant tools adopted in the book ranging from algebra to probability theory, but without exceeding the undergraduate students who wish to be acquainted with number theory, graduate students intending to specialize in this field and researchers requiring the present state of knowledge. |

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Textbook

### Contents

Divisibility Congruences | 1 |

Arithmetical Functions | 53 |

Prime Numbers | 92 |

Sieve Methods | 144 |

Geometry of Numbers | 175 |

Additive Number Theory | 207 |

Probabilistic Number Theory | 241 |

Diophantine Approximation | 281 |

Algebraic Numbers and p Adic Numbers | 303 |

355 | |

369 | |

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### Common terms and phrases

absolutely convergent additive function algebraic integers algebraic number apply arbitrary arithmetical functions asymptotic Chapter character complex numbers congruence contained continued fraction convex set Corollary to Theorem Dedekind ring denote the number density Dirichlet convolution Dirichlet series distribution function divides divisible divisors equality equation estimate exists finite following lemma following theorem formula fractional ideal function f G. H. Hardy gives hence holds inequality infinitely integral coefficients interval isomorphic l(mod lattice Lemma lim sup linear log log minimal polynomial Minkowski's theorem modp moreover multiplicative function natural number non-negative number of primes number theory p-adic integers partial quotient positive number prime ideal prime numbers primitive root Proof properties prove rational integers rational number real numbers result satisfying the condition sequence sieve squares sufficiently large suppose tends to infinity uniformly convergent unique write