The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ...Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions. The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

zlib/Mathematics/Roland van der Veen and Jan van de Craats/The Riemann Hypothesis (Anneli Lax New Mathematical Library)_5345338.pdf

THE RIEMANN HYPOTHESIS A MILLION DOLLAR PROBLEM,ROLAND VAN DER VEEN,LEIDEN UNIVERSITY,JAN VAN DE CRAATS

UNIVERSITY OF AMSTERDAM,THE MATHEMATICAL ASSOCIATION OF AMERICA

Craats, Jan van de; Veen, Roland van der

American Mathematical Society

United States, United States of America

PS, 2015

2016

lg2805055

Roland Van Der Veen And Jan Van De Craats. Original Title: De Riemann-hypothese : Een Miljoenenprobleem, Epsilon Uitgaven, Utrecht, 2011. Translated By The Authors. Includes Bibliographical References And Index.

2020-02-01