# ACTIVITES ADDITIVES ET ANALYTIQUES A LILLE

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English
8 Pages

Description

ACTIVITES ADDITIVES ET ANALYTIQUES A LILLE — 30 JUIN / 4 JUILLET 2009 Overview of the talks Partitions with relatively prime parts and some congruence by Mohammed El Bachraoui A set A of positive integers is relatively prime if gcd(A) = 1. A partition of n is relatively prime if its parts form a relatively prime set. The number of partitions of n into exactly k parts is denoted by p(n, k) and the number of relatively prime partitions into exactly k parts is denoted by p?(n)(n, k). In our talk we will give explicit formulas for p(n, 3) and prove an identity expressing p?(n)(n, 3) in terms of the Jordan's totient function of order 2. Among other things, using the main theorem of our talk we will obtain the following beautiful result. For any prime p > 3, p?(p)(p, 3) = (p 2 ? 1)/12. Smooth values of binary forms by Antal Balog The following type of problem is raised by some cryptographic application. Let F (X,Y ) be a binary form with integer coefficients, and 1 < P < R be real numbers. There are R2 positive integers X,Y ≤ R such that the prime factors of F (X,Y ) are all < P .

• infinite many large

• analogue

• relatively prime

• mobius function

• large integer

• probleme de waring pour les entiers

• arithmetic part

• riemann zeta-function

Subjects