Zeta Functions Over Zeros Of Zeta Functions
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Zeta Functions over Zeros of Zeta Functions
Author: André Voros
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-11-21
In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.
The Riemann Zeta-Function
Author: Anatoly A. Karatsuba
language: en
Publisher: Walter de Gruyter
Release Date: 2011-05-03
No detailed description available for "The Riemann Zeta-Function".
Zeta Functions of Graphs
Author: Audrey Terras
language: en
Publisher: Cambridge University Press
Release Date: 2010-11-18
Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.