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The Distribution of Prime Numbers

2019-12-06 Education
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Release : 2019-12-06
Genre : Education
Kind : eBook
Book Rating : 541/5 ( reviews)

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Book Synopsis The Distribution of Prime Numbers by : Dimitris Koukoulopoulos

Download or read book The Distribution of Prime Numbers written by Dimitris Koukoulopoulos. This book was released on 2019-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources.

The Distribution of Prime Numbers

1990-09-28 Mathematics
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Release : 1990-09-28
Genre : Mathematics
Kind : eBook
Book Rating : 896/5 ( reviews)

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Book Synopsis The Distribution of Prime Numbers by : Albert Edward Ingham

Download or read book The Distribution of Prime Numbers written by Albert Edward Ingham. This book was released on 1990-09-28. Available in PDF, EPUB and Kindle. Book excerpt: 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 Prime Numbers and Their Distribution

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 470/5 ( reviews)

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Book Synopsis The Prime Numbers and Their Distribution by : Gerald Tenenbaum

Download or read book The Prime Numbers and Their Distribution written by Gerald Tenenbaum. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness. The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem. This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

Irregularities in the Distribution of Prime Numbers

2018-07-04 Mathematics
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Release : 2018-07-04
Genre : Mathematics
Kind : eBook
Book Rating : 779/5 ( reviews)

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Book Synopsis Irregularities in the Distribution of Prime Numbers by : János Pintz

Download or read book Irregularities in the Distribution of Prime Numbers written by János Pintz. This book was released on 2018-07-04. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.

The Riemann Hypothesis and the Distribution of Prime Numbers

2021-04-15 Mathematics
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Release : 2021-04-15
Genre : Mathematics
Kind : eBook
Book Rating : 220/5 ( reviews)

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Book Synopsis The Riemann Hypothesis and the Distribution of Prime Numbers by : Naji Arwashan, PhD, PE

Download or read book The Riemann Hypothesis and the Distribution of Prime Numbers written by Naji Arwashan, PhD, PE. This book was released on 2021-04-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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