000 02234nam a22003498i 4500
001 CR9780511760426
003 UkCbUP
005 20200124160220.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 100506s2011||||enk o ||1 0|eng|d
020 _a9780511760426 (ebook)
020 _z9780521113670 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA166
_b.T47 2011
082 0 0 _a511/.5
_222
100 1 _aTerras, Audrey,
_eauthor.
245 1 0 _aZeta functions of graphs :
_ba stroll through the garden /
_cAudrey Terras.
264 1 _aCambridge :
_bCambridge University Press,
_c2011.
300 _a1 online resource (xii, 239 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v128
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520 _aGraph 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.
650 0 _aGraph theory.
650 0 _aFunctions, Zeta.
776 0 8 _iPrint version:
_z9780521113670
830 0 _aCambridge studies in advanced mathematics ;
_v128.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511760426
999 _c516684
_d516682