Anatomy of Integers (CRM Proceedings & Lecture Notes)

Anatomy of Integers (CRM Proceedings & Lecture Notes)


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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 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 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 Gerald Tenenbaum.


Ternary quadratic forms, and sums of three squares with restricted variables by V. Blomer Entiers ayant exactement $r$ diviseurs dans un intervalle donne by R. de la Breteche On the proportion of numbers coprime to a given integer by P. Erdos, F. Luca, and C. Pomerance Integers wtih a divisor in ${(}y,2y{]}$ by K. Ford Power-free values, repulsion between points, differing beliefs and the existence of error by H. A. Helfgott Anatomy of integers and cyclotomic polynomials by H. Maier Parite des valeurs de la fonction de partition $p(n)$ et anatomie des entiers by J.-L. Nicolas The distribution of smooth numbers in arithmetic progressions by K. Soundararajan Moyennes de certaines fonctions multiplicatives sur les entiers friables, 4 by G. Tenenbaum and J. Wu Uniform distribution of zeros of Dirichlet series by A. Akbary and M. R. Murty On primes represented by quadratic polynomials by S. Baier and L. Zhao Descartes numbers by W. D. Banks, A. M. Guloglu, C. W. Nevans, and F. Saidak A combinatorial method for developing Lucas sequence identities by E. Croot On the difference of arithmetic functions at consecutive arguments by J.-M. De Koninck and F. Luca Pretentious multiplicative functions and an inequality for the zeta-function by A. Granville and K. Soundararajan On the distribution of $\omega(n)$ by R. Khan The Erdos-Kac theorem and its generalizations by W. Kuo and Y.-R. Liu On a conjecture on Montgomery-Vaughan on extreme values of automorphic $L$-functions at 1 by J. Liu, E. Royer, and J. Wu The Mobius function in short intervals by N. Ng An explicit approach to hypothesis H for polynomials over a finite field by P. Pollack On prime factors of integers which are sums or shifted products by C. L. Stewart Simultaneous approximation of reals by values of arithmetic functions by E. B. Wong.

Product Details

  • ISBN13: 9780821844069
  • Format: Paperback
  • ID: 9780821844069
  • ISBN10: 0821844067

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