The Riemann Zeta-Function: Theory and Applications

Product Description:

Subjects: Mathematics, Science/Mathematics, Calculus, Mathematics / General, Advanced, Functions, Zeta,

Stalking the zeros
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.

Riemann Zeta Function - Density of Zeros on the Critical Line
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).

a great update of titchmarsh's book
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.
there is some stuff devoted to primes, but the main ideas concern only the analytic results of the zeta function, zero free zones and densities, (higher) power moments, exponential integrals, dirichlet problems, approximate functional equation, critical line, riemann hypothesis...

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)