Articles liés à The Great Prime Number Race

The Great Prime Number Race - Couverture souple

Plymen, Roger

 
9781470462574: The Great Prime Number Race
Couverture souple
ISBN 10 : 1470462575 ISBN 13 : 9781470462574
Editeur : American Mathematical Society, 2021

Synopsis

Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number. This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Roger Plymen, Manchester University, United Kingdom

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2021
Langue
anglais
ISBN 10 
1470462575
ISBN 13 
9781470462574
Reliure
Broché
Nombre de pages
152
Coordonnées du fabricant
non disponible
Personne responsable
non disponible