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Harold M. Edwards
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Riemann's Zeta Function Dover Ed Edition

by Harold M. Edwards (Author)
4.6 4.6 out of 5 stars 171 ratings
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Bernhard Riemann's eight-page paper entitled "On the Number of Primes Less Than a Given Magnitude" was a landmark publication of 1859 that directly influenced generations of great mathematicians, among them Hadamard, Landau, Hardy, Siegel, Jensen, Bohr, Selberg, Artin, and Hecke. This text, by a noted mathematician and educator, examines and amplifies the paper itself, and traces the developments in theory inspired by it. (An English translation of the original document appears in the Appendix.)
Topics include Riemann's main formula, the prime number theorem, de la Vallée Poussin's theorem, numerical analysis of roots by Euler-Maclaurin summation, the Riemann-Siegel formula, largescale computations, Fourier analysis, zeros on the line, the Riemann hypothesis and Farey series, alternative proof of the integral formula, Tauberian theorems, Chebyshev's identity, and other related topics.
This inexpensive edition of Edwards' superb high-level study will be welcomed by students and mathematicians. Mathematically inclined general readers will likewise value this influential classic.

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  1. ISBN-10
    0486417409
  2. ISBN-13
    978-0486417400
  3. Edition
    Dover Ed
  4. Publisher
    Dover Publications
  5. Publication date
    June 13, 2001
  6. Language
    English
  7. Dimensions
    5.43 x 0.69 x 8.52 inches
  8. Print length
    336 pages
  9. See all details
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Product details

  • Publisher ‏ : ‎ Dover Publications; Dover Ed edition (June 13, 2001)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 336 pages
  • ISBN-10 ‏ : ‎ 0486417409
  • ISBN-13 ‏ : ‎ 978-0486417400
  • Item Weight ‏ : ‎ 2.31 pounds
  • Dimensions ‏ : ‎ 5.43 x 0.69 x 8.52 inches
  • Customer Reviews:
    4.6 4.6 out of 5 stars 171 ratings

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Harold M. Edwards

Harold M. Edwards

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Customer reviews

4.6 out of 5 stars
171 global ratings

Customers say

Customers find the textbook useful and well-written on the Riemann Hypothesis. They also mention that the zeta function is dense and well written.

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UsefulnessClarity
13 customers mention "Usefulness"13 positive0 negative

Customers find the book useful for understanding zeta functions. They say the presentation is engaging and deep. They also say it's very technical, giving good motivation for the theory. Customers also mention that it'll be accessible for occasional mathematicians.

"...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..." Read more

"...However, Edward's work is also appropriate for experts and hits the highlights of background leading to the Zeta function...." Read more

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

"...This book is wonderful because it is not just a compendium of results, but explains the evolution of different areas in math resulting from Riemann..." Read more

4 customers mention "Clarity"4 positive0 negative

Customers find the book well-written and an excellent read. They also appreciate the author's straight-forward explanations.

"A very clear and quite easily most complete source of information about the Riemann Zeta function...." Read more

"...The author is very straight and the explanations are clear, though the topic itself is very difficult." Read more

"Excellent read. Great for those interested in the Riemann Hypothesis." Read more

"Well written text on the Riemann Hypothesis..." Read more

Top reviews from the United States

Palle E T Jorgensen
5.0 out of 5 stars New and old.
Reviewed in the United States on April 4, 2003
Verified Purchase
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.
64 people found this helpful
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Bachelier
5.0 out of 5 stars Excellent for experts and the casual mathematician alike
Reviewed in the United States on September 19, 2005
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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.
76 people found this helpful
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Kelly R. Novak
4.0 out of 5 stars The classic book on the subject, but not for everyone.
Reviewed in the United States on August 18, 2017
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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.
16 people found this helpful
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Satisfied Customer
5.0 out of 5 stars Well written text on the Riemann Hypothesis
Reviewed in the United States on April 2, 2021
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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."
3 people found this helpful
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stats guy
5.0 out of 5 stars fascinating
Reviewed in the United States on December 12, 2012
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I consider myself more a user of math results than one who really understands math. This book is wonderful because it is not just a compendium of results, but explains the evolution of different areas in math resulting from Riemann's 8-page paper. I read the first chapter like a dense novel (think Dostoyevsky or Pynchon). I liked it so much that I just order another book by Harold Edwards, the one on "Galois Theory"
9 people found this helpful
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Vinson Paul Milligan
5.0 out of 5 stars My brain feels like the cover after perusing through it
Reviewed in the United States on October 14, 2015
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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.
3 people found this helpful
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positive costumer :)
3.0 out of 5 stars i would say a good book as a reference book of some sorts like ...
Reviewed in the United States on July 16, 2016
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i would say a good book as a reference book of some sorts like when you want some memory refreshing on Riemann zeta function.simply a nice math book certainly not great even say with say subject restrictions and specialty of book. all in all a good math book to read , have a good day and remember read as many books as you can!!!
One person found this helpful
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Stuart Winter
5.0 out of 5 stars For the super brainy only
Reviewed in the United States on October 2, 2014
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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
7 people found this helpful
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Top reviews from other countries

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Joueur 1
5.0 out of 5 stars Les rudiments pour les calculs de somme
Reviewed in France on March 2, 2024
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Ce livre est bien fait le seul hic c est qu il faille le traduire de l anglais mais sinon très complet il aide et donne les rudiments pour la compréhension de la fonction Zêta un des livres a avoir si l on souhaite comprendre cette fonction
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Sekhmet
5.0 out of 5 stars Z
Reviewed in Italy on September 22, 2023
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Ora un pò più di chiarezza sul tema
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V. Putz
5.0 out of 5 stars Hervorragend
Reviewed in Germany on July 26, 2023
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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!
One person found this helpful
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mache
5.0 out of 5 stars Very interseting
Reviewed in Canada on January 21, 2021
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Good and interesting book.
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SANJAY KUMAR
5.0 out of 5 stars Remarkable...
Reviewed in India on October 2, 2017
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Best book on Riemann Zeta Function
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