Ranks of elliptic curves and random matrix theory:
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...
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| Format: | Elektronisch Tagungsbericht E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schriftenreihe: | London Mathematical Society lecture note series
341 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | 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 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (vi, 361 pages) |
| ISBN: | 9780511735158 |
| DOI: | 10.1017/CBO9780511735158 |
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| 505 | 8 | |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 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 -- | |
| 505 | 8 | |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 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 -- | |
| 505 | 8 | |a 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 | |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 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 | ||
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Datensatz im Suchindex
| _version_ | 1804176882677055488 |
|---|---|
| any_adam_object | |
| author2 | Conrey, J. B. |
| author2_role | edt |
| author2_variant | j b c jb jbc |
| author_facet | Conrey, J. B. |
| building | Verbundindex |
| bvnumber | BV043941242 |
| classification_rvk | SI 320 SK 180 SK 240 |
| collection | ZDB-20-CBO |
| contents | 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 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511735158 (OCoLC)850083502 (DE-599)BVBBV043941242 |
| dewey-full | 516.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.352 |
| dewey-search | 516.352 |
| dewey-sort | 3516.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511735158 |
| format | Electronic Conference Proceeding eBook |
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| indexdate | 2024-07-10T07:39:15Z |
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| isbn | 9780511735158 |
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| series2 | London Mathematical Society lecture note series |
| spelling | Ranks of elliptic curves and random matrix theory edited by J.B. Conrey [and others] Ranks of Elliptic Curves & Random Matrix Theory Cambridge Cambridge University Press 2007 1 online resource (vi, 361 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 341 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 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 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 Curves, Elliptic / Congresses Random matrices / Congresses Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Rang Mathematik (DE-588)4176937-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Elliptische Kurve (DE-588)4014487-2 s Rang Mathematik (DE-588)4176937-5 s Stochastische Matrix (DE-588)4057624-3 s 1\p DE-604 Conrey, J. B. edt Isaac Newton Institute for Mathematical Sciences issuing body Sonstige oth Clay Mathematics Institute issuing body Sonstige oth Erscheint auch als Druckausgabe 978-0-521-69964-8 https://doi.org/10.1017/CBO9780511735158 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ranks of elliptic curves and random matrix theory 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 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 Curves, Elliptic / Congresses Random matrices / Congresses Elliptische Kurve (DE-588)4014487-2 gnd Stochastische Matrix (DE-588)4057624-3 gnd Rang Mathematik (DE-588)4176937-5 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4057624-3 (DE-588)4176937-5 (DE-588)1071861417 |
| title | Ranks of elliptic curves and random matrix theory |
| title_alt | Ranks of Elliptic Curves & Random Matrix Theory |
| title_auth | Ranks of elliptic curves and random matrix theory |
| title_exact_search | Ranks of elliptic curves and random matrix theory |
| title_full | Ranks of elliptic curves and random matrix theory edited by J.B. Conrey [and others] |
| title_fullStr | Ranks of elliptic curves and random matrix theory edited by J.B. Conrey [and others] |
| title_full_unstemmed | Ranks of elliptic curves and random matrix theory edited by J.B. Conrey [and others] |
| title_short | Ranks of elliptic curves and random matrix theory |
| title_sort | ranks of elliptic curves and random matrix theory |
| topic | Curves, Elliptic / Congresses Random matrices / Congresses Elliptische Kurve (DE-588)4014487-2 gnd Stochastische Matrix (DE-588)4057624-3 gnd Rang Mathematik (DE-588)4176937-5 gnd |
| topic_facet | Curves, Elliptic / Congresses Random matrices / Congresses Elliptische Kurve Stochastische Matrix Rang Mathematik Konferenzschrift |
| url | https://doi.org/10.1017/CBO9780511735158 |
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