000			04531nam a22003978i 4500
001			CR9780511735158
003			UkCbUP
005			20200124160228.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100325s2007||||enk o ||1 0|eng|d
020			_a9780511735158 (ebook)
020			_z9780521699648 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA567.2.E44 _bR36 2007
082	0	4	_a516.352 _222
245	0	0	_aRanks of elliptic curves and random matrix theory / _cedited by J.B. Conrey [and others].
246	3		_aRanks of Elliptic Curves & Random Matrix Theory
264		1	_aCambridge : _bCambridge University Press, _c2007.
300			_a1 online resource (vi, 361 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v341
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aIntroduction J.B. Conrey, D.W. Farmer, F. Mezzadri and N.C. Snaith -- Part I. Families: Elliptic curves, rank in families and random matrices E. Kowalski -- Modeling families of L-functions D.W. Farmer -- Analytic number theory and ranks of elliptic curves M.P. Young -- The derivative of SO(2N +1) characteristic polynomials and rank 3 elliptic curves N.C. Snaith -- Function fields and random matrices D. Ulmer -- Some applications of symmetric functions theory in random matrix theory A. Gamburd -- Part II. Ranks of Quadratic Twists -- The distribution of ranks in families of quadratic twists of elliptic curves A. Silverberg -- Twists of elliptic curves of rank at least four K. Rubin and A. Silverberg -- The powers of logarithm for quadratic twists C. Delaunay and M. Watkins -- Note on the frequency of vanishing of L-functions of elliptic curves in a family of quadratic twists C. Delaunay -- Discretisation for odd quadratic twists J.B. Conrey, M.O. Rubinstein, N.C. Snaith and M. Watkins -- Secondary terms in the number of vanishings of quadratic twists of elliptic curve L-functions J.B. Conrey, A. Pokharel, M.O. Rubinstein and M. Watkins -- Fudge factors in the Birch and Swinnerton-Dyer Conjecture K. Rubin -- Part III. Number Fields and Higher Twists -- Rank distribution in a family of cubic twists M. Watkins -- Vanishing of L-functions of elliptic curves over number fields C. David, J. Fearnley and H. Kisilevsky -- Part IV. Shimura Correspondence, and Twists -- Computing central values of L-functions F. Rodriguez-Villegas -- Computation of central value of quadratic twists of modular L-functions Z. Mao, F. Rodriguez-Villegas and G. Tornaria -- Examples of Shimura correspondence for level p2 and real quadratic twists A. Pacetti and G. Tornaria -- Central values of quadratic twists for a modular form of weight H. Rosson and G. Tornaria -- Part V. Global Structure: Sha and Descent -- Heuristics on class groups and on Tate-Shafarevich groups C. Delaunay -- A note on the 2-part of X for the congruent number curves D.R. Heath-Brown -- 2-Descent tThrough the ages P. Swinnerton-Dyer.
520			_aRandom matrix theory is an area of mathematics first developed by physicists interested in the energy levels of atomic nuclei, but it can also be used to describe some exotic phenomena in the number theory of elliptic curves. The purpose of this book is to illustrate this interplay of number theory and random matrices. It begins with an introduction to elliptic curves and the fundamentals of modelling by a family of random matrices, and moves on to highlight the latest research. There are expositions of current research on ranks of elliptic curves, statistical properties of families of elliptic curves and their associated L-functions and the emerging uses of random matrix theory in this field. Most of the material here had its origin in a Clay Mathematics Institute workshop on this topic at the Newton Institute in Cambridge and together these contributions provide a unique in-depth treatment of the subject.
650		0	_aCurves, Elliptic _vCongresses.
650		0	_aRandom matrices _vCongresses.
700	1		_aConrey, J. B., _eeditor.
710	2		_aIsaac Newton Institute for Mathematical Sciences, _eissuing body.
710	2		_aClay Mathematics Institute, _eissuing body.
776	0	8	_iPrint version: _z9780521699648
830		0	_aLondon Mathematical Society lecture note series ; _v341.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511735158
999			_c517368 _d517366