The Riemann Hypothesis And The Distribution Of Prime Numbers
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The Riemann Hypothesis and the Distribution of Prime Numbers
Author: Naji Arwashan, PhD, PE
language: en
Publisher: Nova Science Publishers
Release Date: 2021-04-15
This book is an introductory and comprehensive presentation of the Riemann Hypothesis, one of the most important open questions in math today. It is introductory because it is written in an accessible and detailed format that makes it easy to read and understand. And it is comprehensive because it explains and proves all the mathematical ideas surrounding and leading to the formulation of the hypothesis.
The Distribution of Prime Numbers
Author: Albert Edward Ingham
language: en
Publisher: Cambridge University Press
Release Date: 1990-09-28
Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
THE SYMPHONY OF PRIMES, DISTRIBUTION OF PRIMES AND RIEMANN'S HYPOTHESIS
This book presents research results concerning the distribution of prime numbers. The first major result discussed is the supremum for the maximal prime gaps. By an implementation of a binomial coefficient the maximal prime gaps supremum bound is proved, simultaneously establishing the infimum for primes in the short interval. Subsequently, a novel application of the theory of the primorial function establishes the tailored logarithmic integral, which is a superior adaptation of the classical Gauss' logarithmic integral. The tailored integral due to its radically improved accuracy over the Gauss' logarithmic integral, constitutes the supremum bound of estimation of the prime counting function. It presents the possibility to estimate the prime counting function with unprecedented accuracy.