Softcover ISBN:  9780821844069 
Product Code:  CRMP/46 
List Price:  $112.00 
MAA Member Price:  $100.80 
AMS Member Price:  $89.60 
Electronic ISBN:  9781470439606 
Product Code:  CRMP/46.E 
List Price:  $105.00 
MAA Member Price:  $94.50 
AMS Member Price:  $84.00 

Book DetailsCRM Proceedings & Lecture NotesVolume: 46; 2008; 297 ppMSC: Primary 11;
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 functions such as the partition function. More specific topics include the Erdős–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 and unexpected consequences. The volume includes contributions from leading participants in this active area of research, such as Kevin Ford, Carl Pomerance, Kannan Soundararajan and Gérald Tenenbaum.
ReadershipUndergraduates and graduate students and research mathematicians interested in Erdős–type elementary number theory, smooth numbers, and distribution of prime factors of integers, partitions, etc.

Table of Contents

Chapters

Ternary quadratic forms, and sums of three squares with restricted variables

Entiers ayant exactement $r$ diviseurs dans un intervalle donné

On the proportion of numbers coprime to a given integer

Integers with a divisor in ${(}y,2y{]}$

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

Anatomy of integers and cyclotomic polynomials

Parité des valeurs de la fonction de partition $p(n)$ et anatomie des entiers

The distribution of smooth numbers in arithmetic progressions

Moyennes de certaines fonctions multiplicatives sur les entiers friables, 4

Uniform distribution of zeros of Dirichlet series

On primes represented by quadratic polynomials

Descartes numbers

A combinatorial method for developing Lucas sequence identities

On the difference of arithmetic functions at consecutive arguments

Pretentious multiplicative functions and an inequality for the zetafunction

On the distribution of $\omega (n)$

The Erdős–Kac theorem and its generalizations

On a conjecture of MontgomeryVaughan on extreme values of automorphic $L$functions at 1

The Möbius function in short intervals

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

On prime factors of integers which are sums or shifted products

Simultaneous approximation of reals by values of arithmetic functions


Additional Material

Reviews

[I]t is quite satisfying to read in these papers some pretty descriptions of the insights behind the methods of proof, so that the application of technical anatomical results seems natural rather than confounding.
Greg Martin, University of British Columbia


RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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 functions such as the partition function. More specific topics include the Erdős–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 and unexpected consequences. The volume includes contributions from leading participants in this active area of research, such as Kevin Ford, Carl Pomerance, Kannan Soundararajan and Gérald Tenenbaum.
Undergraduates and graduate students and research mathematicians interested in Erdős–type elementary number theory, smooth numbers, and distribution of prime factors of integers, partitions, etc.

Chapters

Ternary quadratic forms, and sums of three squares with restricted variables

Entiers ayant exactement $r$ diviseurs dans un intervalle donné

On the proportion of numbers coprime to a given integer

Integers with a divisor in ${(}y,2y{]}$

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

Anatomy of integers and cyclotomic polynomials

Parité des valeurs de la fonction de partition $p(n)$ et anatomie des entiers

The distribution of smooth numbers in arithmetic progressions

Moyennes de certaines fonctions multiplicatives sur les entiers friables, 4

Uniform distribution of zeros of Dirichlet series

On primes represented by quadratic polynomials

Descartes numbers

A combinatorial method for developing Lucas sequence identities

On the difference of arithmetic functions at consecutive arguments

Pretentious multiplicative functions and an inequality for the zetafunction

On the distribution of $\omega (n)$

The Erdős–Kac theorem and its generalizations

On a conjecture of MontgomeryVaughan on extreme values of automorphic $L$functions at 1

The Möbius function in short intervals

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

On prime factors of integers which are sums or shifted products

Simultaneous approximation of reals by values of arithmetic functions

[I]t is quite satisfying to read in these papers some pretty descriptions of the insights behind the methods of proof, so that the application of technical anatomical results seems natural rather than confounding.
Greg Martin, University of British Columbia