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170324  eng 
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a 9780511735158

050 

4 
a QA567.2.E44

100 
1 

a Conrey, J. B.
e [editor]

245 
0 
0 
a Ranks of elliptic curves and random matrix theory
c edited by J.B. Conrey [and others]

246 
3 
1 
a Ranks of Elliptic Curves & Random Matrix Theory

260 


a Cambridge
b Cambridge University Press
c 2007

300 


a vi, 361 pages
b digital

505 
0 

a Introduction 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 Lfunctions 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 Lfunctions of elliptic curves in a family of quadratic twists C. Delaunay 

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0 

a 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 Lfunctions J.B. Conrey, A. Pokharel, M.O. Rubinstein and M. Watkins  Fudge factors in the Birch and SwinnertonDyer Conjecture K. Rubin  Part III. Number Fields and Higher Twists  Rank distribution in a family of cubic twists M. Watkins  Vanishing of Lfunctions of elliptic curves over number fields C. David, J. Fearnley and H. Kisilevsky  Part IV. Shimura Correspondence, and Twists  Computing central values of Lfunctions F. RodriguezVillegas  Computation of central value of quadratic twists of modular Lfunctions Z. Mao, F. RodriguezVillegas 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 

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a Part V. Global Structure: Sha and Descent  Heuristics on class groups and on TateShafarevich groups C. Delaunay  A note on the 2part of X for the congruent number curves D.R. HeathBrown  2Descent tThrough the ages P. SwinnertonDyer

653 


a Curves, Elliptic / Congresses

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a Random matrices / Congresses

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a Isaac Newton Institute for Mathematical Sciences

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a Clay Mathematics Institute

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7 
a eng
2 ISO 6392

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b CBO
a Cambridge Books Online

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a London Mathematical Society lecture note series

028 
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a 10.1017/CBO9780511735158

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u https://doi.org/10.1017/CBO9780511735158
x Verlag
3 Volltext

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0 

a 516.352

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a Random 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 Lfunctions 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 indepth treatment of the subject
