» Riemann's Zeta Function

Riemann's Zeta Function Reviews

Customer Rating:
Summary: Very Technical
Comment: 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.

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Customer Rating:
Summary: a famous function unravelled
Comment: a wonderful exposition full of incredible formulae; a careful account of what Riemann could have thought of when writing his famous paper; the text contains calculations of zeta's non trivial zeroes in an old fashion way but still illuminating. Lacks schema of contours used in calculating
complex integrals but this is a very minor flaw; on the other side, one can find copies of two pages handwritten by B. Riemann which may show how casually this great genius could work and may explain why his followers had such difficulties in proving and following his ideas; the study of zeta means some herculean calculations of which Edwards gives a fine taste; this book is worth the pain to work with; one can compare his first proof of zeta's functional equation with those given in Ahlfors's "Complex analysis" or Tenenbaum's book: "Introduction to analytic an probabilistic theory of numbers"; my favourite formulae are:
1) Von Mangoldt's formula for the psi function with summation over the nontrivial zeroes of zeta.
2) the formula for the product of zeta and gamma as an improper integral and its sequel using hankel contour.
3) the Siegel-Riemann formula for Z(t), this Z function being derived from the values of zeta on the line re(z) = 1/2.
This is the very book to remove oneself on a desert island with (but don't forget a laptop to verify tha accuracy of Backlund's estimations of the fifteen first non trivial zeroes of ... zeta.
By the way, do you happen to know which are the trivial zeroes ?

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Customer Rating:
Summary: Protestation
Comment: Comme vous auriez pu vous en douter, vu l'adresse où vous avez envoyé le livre, je suis français
Ecrivez moi en français, et je vous répondrai

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Customer Rating:
Summary: Riemann Zeta Function & The Riemann Hypothesis
Comment: Undoubtedly the best technical exposition on the Riemann Zeta Function, complete with derivations, proofs, and examples of calculations. As a special treat, it includes a translation of Riemann's original paper on the Zeta function, a photocopy of one page of Riemann's notes, and detailed references to papers of earlier authors of papers and books on the Riemann Zeta function, including a table of values of zeta(½ + it) for t=0 to 50 in increments of 0.2 [Haselgrove, Royal Society Math Tables, Cambridge Univ. Press, 1960].

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Customer Rating:
Summary: A fascinating journey of discovery
Comment: I had a hard time putting this book down. Who would have thought that for a book about mathematicians and a function? Ok, I am a mathematician and physicist, but still, this really brought to life the exploration and probing of the bizarre and fascinating universe we have created in mathematics.

I highly recommend this book to anyone who likes the history of science and mathematics and is excited by discovery. Even if you only know algebra, I believe that you'll be able to follow the key mathematical concepts and implications.

(Note: four stars is a really, really good rating from me. I haven't given a five star rating yet, which is reserved for literature that is truly mind-blowing.)

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