## Anatomy of IntegersJ. M. de Koninck, Andrew Granville, Florian Luca The book is mostly devoted to the study of the prime factors of integers, their size and their quantity, to good bounds on the number of integers with different properties (for example, those with only large prime factors) and to the distribution of divisors of integers in a given interval. In particular, various estimates concerning smooth numbers are developed. A large emphasis is put on the study of additive and multiplicative functions as well as various arithmetic functionssuch as the partition function. More specific topics include the Erdos-Kac Theorem, cyclotomic polynomials, combinatorial methods, quadratic forms, zeta functions, Dirichlet series and $L$-functions. All these create an intimate understanding of the properties of integers and lead to fascinating andunexpected consequences. The volume includes contributions from leading participants in this active area of research, such as Kevin Ford, Carl Pomerance, Kannan Soundararajan and Gerald Tenenbaum. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

vii | |

1 | |

Entiers ayant exactement r diviseurs dans un intervalle donné | 19 |

On the proportion of numbers coprime to a given integer | 47 |

Integers with a divisor in y 2y | 65 |

Powerfree values repulsion between points differing beliefs and the existence of error | 81 |

Anatomy of integers and cyclotomic polynomials | 89 |

Parité des valeurs de la fonction de partition pn et anatomie des entiers | 97 |

Descartes numbers | 167 |

A combinatorial method for developing Lucas sequence identities | 175 |

On the difference of arithmetic functions at consecutive arguments | 179 |

Pretentious multiplicative functions and an inequality for the zetafunction | 191 |

On the distribution of 𝛚n | 199 |

The ErdosKac theorem and its generalizations | 209 |

On a conjecture of MontgomeryVaughan on extreme values of automorphic Lfunctions at 1 | 217 |

The Môbius function in short intervals | 247 |

The distribution of smooth numbers in arithmetic progressions | 115 |

Moyennes de certaines fonctions multiplicatives sur les entiers friables 4 | 129 |

Uniform distribution of zeros of Dirichlet series | 143 |

On primes represented by quadratic polynomials | 159 |

An explicit approach to hypothesis H for polynomials over a finite field | 259 |

On prime factors of integers which are sums or shifted products | 275 |

Simultaneous approximation of reals by values of arithmetic functions | 289 |

### Common terms and phrases

2000 Mathematics Subject 2008 American Mathematical Acta Arith Andrew Granville assume asymptotic formula avons character coefficients completes the proof Conjecture 1.1 coprime Corollary CRM Proceedings cyclotomic polynomials deduce define défini démonstration Density Hypothesis Dirichlet Dirichlet series E-mail address entiers Erdos Erdos-Kac theorem estimate exists finite follows forme modulaire Granville inequality integers irreducible irreducible polynomial L-functions Lecture Notes Volume Lemma lemme log log log2 logx Math Mathematics Subject Classification mod q modulo monic multiplicative function natural numbers nombres premiers Notes Volume 46 number of prime number theory obtain obtenons polynomials Pomerance positive constant positive integers positive number prime divisors prime factors prime number prime number theorem Proceedings and Lecture proof of Theorem Proposition prove quadratic forms result résultat Riemann Hypothesis satisfying Selberg class sequence sieve Soundararajan square squarefree Tenenbaum Theorem 1.2 théorème tout uniformly upper bound values