000 02550nam a22003738i 4500
001 CR9780511983399
003 UkCbUP
005 20200124160239.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 101124s1997||||enk o ||1 0|eng|d
020 _a9780511983399 (ebook)
020 _z9780521445207 (hardback)
020 _z9780521058070 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA246
_b.M78 1997
082 0 0 _a512/.73
_220
100 1 _aMotohashi, Y.
_q(Yoichi),
_eauthor.
245 1 0 _aSpectral theory of the Riemann zeta-function /
_cYoichi Motohashi.
264 1 _aCambridge :
_bCambridge University Press,
_c1997.
300 _a1 online resource (ix, 228 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge tracts in mathematics ;
_v127
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _aConvention and assumed background -- 1. Non-Euclidean harmonics -- 2. Trace formulas -- 3. Automorphic L-functions -- 4. An explicit formula -- 5. Asymptotics.
520 _aThe Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.
650 0 _aFunctions, Zeta.
650 0 _aSpectral theory (Mathematics)
776 0 8 _iPrint version:
_z9780521445207
830 0 _aCambridge tracts in mathematics ;
_v127.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511983399
999 _c518380
_d518378