- Series: Dover Books on Mathematics
- Paperback: 336 pages
- Publisher: Dover Publications; Dover Ed edition (June 13, 2001)
- Language: English
- ISBN-10: 0486417409
- ISBN-13: 978-0486417400
- Product Dimensions: 0.8 x 5.8 x 8.8 inches
- Shipping Weight: 12 ounces (View shipping rates and policies)
- Average Customer Review: 4.7 out of 5 stars See all reviews (32 customer reviews)
- Amazon Best Sellers Rank: #359,708 in Books (See Top 100 in Books)
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Riemann's Zeta Function Dover Ed Edition
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Top Customer Reviews
It includes a translation of Riemann's original paper (On the Number of Primes...) which is very nice and most authors now seem to forget to mention (mainly because of the obscure way in which it was written).
The first chapter is devoted to the study of the paper, then it is followed another chapter proving the product formula (which was not quite proven by Riemann), then a third chapter of von Mangoldt's proof of Riemann's Prime Formula.
The fourth chapter has the famous prime number theorem and it's original proof by Hadamard and Poussin. The fifth one includes an error estimation due to Poussin for the prime number theorem, and the equivalent of the Riemann Hypothesis in terms of prime distributions.
The Euler-Maclaurin formula is introduced in the sixth chapter to calculate zeros in the critical line.
The Riemann-Siegel formula is introduced in the seventh, and then later chapters include large scale computations, Fourier analysis, growth and location of zeros.
Finally we have my favourite chapter, counting zeros: Hardy's theorem, which says that there are infinitely many zeros in the critical line, which was improved by Littlewood, then later by Selberg, and then by Levinson.
The last chapter is dedicated to some theorems, including an elementary proof of the prime number theorem.
Most important idea: the introduction! It will give you an idea of how these amazing people studied and did math.
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.
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.
Most Recent Customer Reviews
i would say a good book as a reference book of some sorts like when you want some memory refreshing on Riemann zeta function. Read morePublished 6 days ago by Amazon Customer
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... Read morePublished 19 days ago by Sridhar Seshagiri
The math is over my head but the explanations are helpful and clear and are giving me a good sense of the process a brilliant mathematician goes through in his explorations. Read morePublished 8 months ago by Amazon Customer
Everything you need to know about the zeta function in a dense, thorough textbook. My brain feels like the cover after perusing through it. Read morePublished 9 months ago by Vinson Paul Milligan
Excellent read. Great for those interested in the Riemann Hypothesis.Published 16 months ago by fnc314