20,108 research outputs found
Nicolaas Govert de Bruijn, the enchanter of friable integers
N.G. de Bruijn carried out fundamental work on integers having only small
prime factors and the Dickman-de Bruijn function that arises on computing the
density of those integers. In this he used his earlier work on linear
functionals and differential-difference equations. We review the relevant work
and also some later improvements by others.Comment: 34 pages, 1 Figur
Levels of Distribution and the Affine Sieve
This article is an expanded version of the author's lecture in the Basic
Notions Seminar at Harvard, September 2013. Our goal is a brief and
introductory exposition of aspects of two topics in sieve theory which have
received attention recently: (1) the spectacular work of Yitang Zhang, under
the title "Level of Distribution," and (2) the so-called "Affine Sieve,"
introduced by Bourgain-Gamburd-Sarnak.Comment: 34 pages, 2 figure
Discrete logarithms in curves over finite fields
A survey on algorithms for computing discrete logarithms in Jacobians of
curves over finite fields
- …