Comprehensive and coherent, this text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, distribution of primes, Dirichlet and various other divisor problems, and more. 1985 edition.
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30 of 32 people found the following review helpful:
5.0 out of 5 stars
a great update of titchmarsh's book,
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This review is from: The Riemann Zeta-Function: Theory and Applications (Dover Books on Mathematics) (Paperback)
this is book is an udpate of the book of titchmarsh (the theory of the riemann zeta function). it covers all the results from 1957 to 1985 (up to atkinson's formula).if you are looking for stuff about prime numbers, or the prime number distribution, this book will only cover a tiny bit. like titchmarsh, ivic normally proves all theorems without assuming riemann or lindelof hypothesis.. there's a chapter where he assumes RH. cool book, it used to be out of print, so i recommend it.. (also titchmarsh, edwards and ingham)
9 of 9 people found the following review helpful:
4.0 out of 5 stars
Riemann Zeta Function - Density of Zeros on the Critical Line,
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This review is from: The Riemann Zeta-Function: Theory and Applications (Dover Books on Mathematics) (Paperback)
A very good technical exposition on the Riemann Zeta function, and it's applications, with emphasis on zero-free regions, the density of zeros on the critical line, and higher power moments of the Zeta function, but is weak on the computation aspects of calculating the zeros of the Zeta function, and only briefly characterizes the Riemann-Siegel Z formula. It contains copious proofs and technical notes, but also includes three pages of errata that have not yet been incorporated into the text (twenty years later).
4 of 4 people found the following review helpful:
4.0 out of 5 stars
Stalking the zeros,
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This review is from: The Riemann Zeta-Function: Theory and Applications (Dover Books on Mathematics) (Paperback)
This is a COMPREHENSIVE compendium of facts, theory, and some history of the Riemann Zeta function. It is organized formally, i. e. Lemmas and Theorems, and the effort will be a little steep for someone not trained in
higher math. On the other hand, this plus H. M. Edwards' book "Riemann's Zeta Function" will have everything needed for casual work on the subject. Ivic's book is highly recommended.
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