Everything you need to know about the zeta function in a dense, thorough textbook. My brain feels like the cover after perusing through it. How can something so simple have an immense complex array of properties underneath of it. This book explains that in a thorough way. Warning: you need to know a bit of the language of math and calculus to understand it fully.

The popular press leaves us with the impression that math is

intimidating. This wasn't always the case. In my time, the approach to how we teach math went thru cycles: (1) The boot-camp

approach with its endless drills, (2) The New-Math approach, (3) The back-to-basics trend, and (4) The Make-it-Seem-Easy-and Fun approach and the motivational speakers.---Finally Edwards suggests, following Eric Temple Bell, that we rather begin with the classics when approaching a subject in math. It was thought that later books based on the classics had more effective ways of doing it, and few took the trouble of looking at the original and central papers of the great masters. The landmark papers. All the while, they collected dust on the shelves in the back rooms of libraries. Of the classics, the true landmarks, one stands out: It is Riemann's paper on the prime numbers, what later turned into the prime number theorem. It is also the paper with the Riemann hypothesis, still unproved, now generations later. So it is a delightful idea including Riemann's paper, in translation, in an appendix. It would have been nice had Edwards also reproduced the original German text. Now the RH is one of the Million-Dollar problems in math. It is anyone's guess when it will be cracked, but in the mean time, it continues to inspire generations of mathematicians and students. This Dover edition is came out in 2001. The original first 1974 edition, Academic Press, had gone out of print. This lovely book seems still to be a model that we can measure other books against. Edwards' presentation is both engaging and deep, and the book contains the gems in a subject that continues to be central in math, the subject of analytic number theory.

This is the classic book on the matter, and I did learn things that I did not already know about it.

However, the audience is targeted, it seems, to those with a Math Ph.D. I have an advanced degree in physics, and I am entirely fascinated with the zeta function and study it a lot. But he lost me in places and I see that other readers could not follow him either in places. And thus, I cannot give him top marks.

I hesitate to add to the chorus of praise here for H.M. Edwards's "Riemann's Zeta Function," for what little mathematics I have is self taught. Nevertheless, after reading John Derbyshire's gripping "Prime Obsession" and following the math he used there with ease, I thought to tackle a more challenging book on the subject. A Topologist friend suggested Titchmarsh's "The Theory of the Riemann Zeta-Function," but I soon bogged down. I happily came across Edwards while browsing, and was pleased both with the low price, and the lucid contents.

For those who are mathematicians and like their introductions to the most fascinating math problems straight and touching all horizons of inquiry, then experts appear to have converged on Titchmarsh as the volume for the first string. However, Edward's work is also appropriate for experts and hits the highlights of background leading to the Zeta function. But Edward's chief strength is beyond his intended audience, for it is his accessibility for the occasional mathematician. With some patience, and not without some little pain and an occasional side trip to "The World of Mathematics" or "The Encyclopedia of Mathematics," even a self-trained mathematician can appreciate most of what Edwards is explaining.

In short, I heartily recommend to those who have enjoyed John Derbyshire's "Prime Obsession," and have additional steam, to take up Edward's "Riemann' Zeta Function" volume for further insights and knowledge.

A very clear and quite easily most complete source of information about the Riemann Zeta function. What I liked most as another reviewer pointed out is "It will give you an idea of how these amazing people studied and did math. "

While this is a strong mathematical treatment of Riemann's Zeta function, the steps between equations are very terse and not intuitively obvious. A little more time could have been spent filling in steps between equations. This is not a book to read but to study. If you have not had graduate level mathematics, choose another book.

Maybe I'm getting old, but the print is very small for the formulae. Especially the exponents.

So you might need a new pair of reading glasses.

As one other reviewer expounded, I am also stuck on the first contour integral,

so I will use his suggested reference.

At the end of the day, you're not going to buy this book unless you have some background in Number Theory and Complex Analysis, so it's going to be challenging.

Beware: any book without the words "Introduction to ..." in the title.

Not for the faint-hearted

A classic written about the properties of the Riemann Zeta function and the greatest unsolved mathematical problem this century - the Riemann Hypothesis. If you have your sites on attempting to solve this problem or just interested in understanding the problem , "this book is the definitive starting point."

Analitik sayı teorisiyle ilgilenen biri olarak söyleyebilirim ki, H. M. Edwards'ın Riemann's Zeta Function kitabı bu alanda yazılmış en önemli klasiklerden biri. Riemann Zeta Fonksiyonu'nu yalnızca teknik yönüyle ele almıyor; tarihsel gelişimini, arkasındaki matematiksel motivasyonu ve analitik sayı teorisindeki yerini de son derece başarılı bir şekilde aktarıyor. Özellikle fonksiyonel denklem, analitik devam ve asal sayıların dağılımıyla olan ilişkisini işlerken sunduğu bakış açısı gerçekten etkileyici.

Kitabın en güçlü yanı, okuyucuyu yalnızca teorem ve ispatlarla baş başa bırakmaması. İspatların neden bu şekilde kurulduğunu, hangi fikirlerden doğduğunu ve matematiksel sezgiyi de aktarmaya çalışıyor. Bu nedenle sadece bir referans kitabı değil, aynı zamanda konuyu gerçekten anlamaya yardımcı olan bir eser. Kompleks analiz ve temel analitik sayı teorisi altyapısı olan herkesin mutlaka okuması gerektiğini düşünüyorum.

Tek eleştirim fiziksel baskı kalitesine yönelik. Sayfalar beklediğimden ince olduğu için arka yüzdeki yazılar yer yer belirgin şekilde görünüyor. Özellikle yoğun formüllerin bulunduğu sayfalarda bu durum uzun süre okurken biraz dikkat dağıtabiliyor. Kitabın akademik değeri tartışılmaz olsa da, böylesine önemli bir eserin daha kaliteli kâğıt ve baskıyla sunulmasını beklerdim.

İçerik açısından benim için tartışmasız 5 yıldızlık bir başyapıt. Ancak baskı kalitesi nedeniyle 1 yıldız kırarak 4 yıldız veriyorum. Eğer analitik sayı teorisiyle ciddi şekilde ilgileniyorsanız veya Riemann Zeta Fonksiyonu üzerine derinlemesine çalışmayı düşünüyorsanız, baskı kusurunu göze alarak yine de gönül rahatlığıyla tavsiye ederim. Bu kitap yıllarca dönüp dönüp başvurulacak nitelikte bir kaynak.

Good and interesting book.

Endlich mal ein Lehrbuch, das man von der ersten bis zur letzten Seite bis ins Detail (fast) vollständig nachvollziehen kann, ohne die in den meisten Büchern doch recht beliebten Sprünge, Lücken oder Formeln "ohne Beweis", die die Sache in eine Glaubenssache verwandeln. Teilweise nicht einfach zu verstehen, aber es lohnt sich!

* Physical

This book has around 315 pages of standard quality paper with few graphs.

* Target audience, H.N.D, undergraduate, graduate, post graduate, Masters?

In my opinion, this book as aimed post graduate, Masters level in Mathematical studies.

* What's the best bits?

The Zeta function has many forms. It is based on Euler's Harmonic series; but is used with real and complex power values instead. Euclid stated that every integer number can be made with a unique compound of prime numbers multiplied together. This linkage between using generating series to see when the real and complex numbers change signs is how to to see when a prime is created. This method of attack uses when this breaking down is explored with instead elemental, basic series to make it easier to get along with.

These workings will be undertaken using mathematical shorthand using greek letters that help to simplify the math, but this is a skill to be learnt in itself. Its then explained with proofs using these elemental series components and mathematical short hand too in a very dense exploration of this area. One topic earlier on is estimating the density of the number of primes, and how the accuracy has been improved upon again and again.This takes a few chapters that is amazing to go through. Fourier series is partially explored. Some of the formulae are to be taken on faith as this would burden the reader too much.

The main burden of math in this book i would is classed as dense. The roots of the Zeta function used with calculating prime numbers is explained and explored to allow the reader to try this out. Its really fun if you keep at it. Amazingly, in the Appendix, page 299 - 305, the translated paper 'On the Number of Primes less than a Given Magnitude' written by Bernhard Riemann is included.

* Aids to help studying this topic

I have been concentrating reading this book for a few months. And i am over halfway through this book. But i have some comprehension and feel like sharing my works so far. It's taken a lot of time to explore this book. It's a hell of a lot of topics to take in and explore. It's been a revelation on appreciating prime numbers, mathematical exploration using a more complex vocabulary using simplified series and topics in proofs and then put together to build upon more concepts.

A well known video sharing website has videos which explore the Zeta series that is, in my opinion, recommended and almost mandatory to help in this topic. Another well known website has mathematical applications of Zeta topics through using its own mathematical CADs pages.

* Summary

This book is not my first in the Zeta area. These other books were written for a wider, more general audience, and not this intensive in their strategy. I am not sure if this is the best, the easiest or most relevant. It's, in my opinion, a deep exploration of this area that does not cover all the fields available to it.

Update: I have been reading and studying this book for over 6 months. The time taken is mostly daily and a few hours per day. I have assimilated as much as i can and still not grasped it all. This is a tough topic but is fascinating. i need a break from it as i reached as far as i can at the moment. This break may may make my mind sharp again and not swimming in proofs that are in depth. If you're doing well, pat yourself on the back for your tenacity!

Un libro leggendario