The analysis of many number theoretic algorithms turns on the role played by integers which
have only small prime factors; such integers are known as “smooth numbers”. To be able to …

In 1918 Pólya and Vinogradov gave an upper bound for the maximal size of character sums,
which still remains the best known general estimate. One of the main results of this paper …

In this paper we investigate the distribution of values of L (1, chi) as chi ranges over primitive
real characters. In particular we focus on the extent to which this distribution may be …

The book introduces new techniques that imply rigorous lower bounds on the com plexity of
some number-theoretic and cryptographic problems. It also establishes certain attractive …

The study of the distribution values of L-functions at the point s= 1 is a classical topic in
analytic number theory which goes back to Chowla and Erdös. For some time, this question …

arXiv:0708.3990v2 [math.NT] 4 Apr 2008 Page 1 arXiv:0708.3990v2 [math.NT] 4 Apr 2008
EXTREME VALUES OF ZETA AND L-FUNCTIONS K. Soundararajan 1. Introduction In this …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

,(1) elles-même liée aux majorations de certains polynômes de Dirichlet eta celles de
maximums localisés de la fonction zêta de Riemann sur la droite verticale d'abscisse α. Soit …

We show that for a Steinhaus random multiplicative function f: N→ D and any polynomial P
(x)∈ Z [x] of deg P≥ 2 which is not of the form w (x+ c) d for some w∈ Z, c∈ Q, we have 1 …

We prove that if is a Steinhaus or Rademacher random multiplicative function, there almost
surely exist arbitrarily large values of for which. This is the first such bound that grows faster …