000 02323nam a22003738i 4500
001 CR9781107238992
003 UkCbUP
005 20200124160224.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 130417s2014||||enk o ||1 0|eng|d
020 _a9781107238992 (ebook)
020 _z9781107047211 (hardback)
020 _z9781107685314 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA246
_b.V36 2014
082 0 0 _a512.73
_223
100 1 _aVan Frankenhuysen, Machiel,
_d1967-
_eauthor.
245 1 4 _aThe Riemann hypothesis for function fields :
_bFrobenius flow and shift operators /
_cMachiel van Frankenhuijsen, Utah Valley University.
264 1 _aCambridge :
_bCambridge University Press,
_c2014.
300 _a1 online resource (xii, 152 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aLondon Mathematical Society student texts ;
_v80
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520 _aThis book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point counting function as a trace of a shift operator on the additive space, and a discussion of how to obtain the explicit formula from the action of the idele class group on the space of adele classes. The exposition is accessible at the graduate level and above, and provides a wealth of motivation for further research in this area.
650 0 _aRiemann hypothesis.
650 0 _aNoncommutative differential geometry.
650 0 _aAlgebraic fields.
776 0 8 _iPrint version:
_z9781107047211
830 0 _aLondon Mathematical Society student texts ;
_v80.
856 4 0 _uhttps://doi.org/10.1017/CBO9781107238992
999 _c517037
_d517035