HomeGroupsTalkZeitgeist
Hide this

Results from Google Books

Click on a thumbnail to go to Google Books.

The Prime Numbers and Their Distribution by…
Loading...

The Prime Numbers and Their Distribution

by Gerald Tenenbaum, Gérald Tenenbaum

MembersReviewsPopularityAverage ratingConversations
16None615,960 (2.5)None

None.

None
Loading...

Sign up for LibraryThing to find out whether you'll like this book.

No current Talk conversations about this book.

No reviews
no reviews | add a review

» Add other authors (7 possible)

Author nameRoleType of authorWork?Status
Gerald Tenenbaumprimary authorall editionscalculated
Tenenbaum, Géraldmain authorall editionsconfirmed
You must log in to edit Common Knowledge data.
For more help see the Common Knowledge help page.
Series (with order)
Canonical title
Original title
Alternative titles
Original publication date
People/Characters
Important places
Important events
Related movies
Awards and honors
Epigraph
Dedication
First words
Quotations
Last words
Disambiguation notice
Publisher's editors
Blurbers
Publisher series
Original language

References to this work on external resources.

Wikipedia in English (1)

Book description
Haiku summary

Amazon.com Product Description (ISBN 0821816470, Paperback)

We have been curious about numbers--and prime numbers--since antiquity. 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. There are two ways in which the book is exceptional. First, some familiar topics are covered with refreshing insight and/or from new points of view. Second, interesting recent developments and ideas are presented that shed new light on the prime numbers and their distribution among the rest of the integers. The book begins with a chapter covering some classic topics, such as quadratic residues and the Sieve of Eratosthenes. Also discussed are other sieves, primes in cryptography, twin primes, and more. Two separate chapters address the asymptotic distribution of prime numbers. In the first of these, the familiar link between $\zeta(s)$ and the distribution of primes is covered with remarkable efficiency and intuition. The later chapter presents a walk through an elementary proof of the Prime Number Theorem. To help the novice understand the "why" of the proof, connections are made along the way with more familiar results such as Stirling's formula. A most distinctive chapter covers the stochastic properties of prime numbers. The authors present a wonderfully clever interpretation of primes in arithmetic progressions as a phenomenon in probability. They also describe Cramér's model, which provides a probabilistic intuition for formulating conjectures that have a habit of being true. In this context, they address interesting questions about equipartition modulo $1$ for sequences involving prime numbers. The final section of the chapter compares geometric visualizations of random sequences with the visualizations for similar sequences derived from the primes. The resulting pictures are striking and illuminating. The book concludes with a chapter on the outstanding big conjectures about prime numbers. 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. This book is the English translation of the French edition.

(retrieved from Amazon Thu, 12 Mar 2015 18:22:51 -0400)

No library descriptions found.

Quick Links

Swap Ebooks Audio
2 wanted

Popular covers

Rating

Average: (2.5)
0.5
1
1.5
2
2.5 1
3
3.5
4
4.5
5

Is this you?

Become a LibraryThing Author.

 

About | Contact | Privacy/Terms | Help/FAQs | Blog | Store | APIs | TinyCat | Legacy Libraries | Early Reviewers | Common Knowledge | 119,454,350 books! | Top bar: Always visible