Hyperelliptic Curves, L-Polynomials, and Random Matrices
We analyze the distribution of unitarized L-polynomials Lp(T) (as p varies) obtained from a hyperelliptic curve of genus g [less than or equal to] 3 defined over Q. In the generic case, we find experimental agreement with a predicted correspondence (based on the Katz-Sarnak random matrix model) be...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Mathematical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/64701 |
| _version_ | 1826214012635840512 |
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| author | Kedlaya, Kiran S. Sutherland, Andrew Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kedlaya, Kiran S. Sutherland, Andrew Victor |
| author_sort | Kedlaya, Kiran S. |
| collection | MIT |
| description | We analyze the distribution of unitarized L-polynomials Lp(T)
(as p varies) obtained from a hyperelliptic curve of genus g [less than or equal to] 3 defined over Q. In the generic case, we find experimental agreement with a predicted correspondence
(based on the Katz-Sarnak random matrix model) between the
distributions of Lp(T) and of characteristic polynomials of random matrices
in the compact Lie group USp(2g). We then formulate an analogue of the
Sato-Tate conjecture for curves of genus 2, in which the generic distribution is
augmented by 22 exceptional distributions, each corresponding to a compact
subgroup of USp(4). In every case, we exhibit a curve closely matching the
proposed distribution, and can find no curves unaccounted for by our classification. |
| first_indexed | 2024-09-23T15:58:24Z |
| format | Article |
| id | mit-1721.1/64701 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:58:24Z |
| publishDate | 2011 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/647012022-09-29T17:23:38Z Hyperelliptic Curves, L-Polynomials, and Random Matrices Kedlaya, Kiran S. Sutherland, Andrew Victor Massachusetts Institute of Technology. Department of Mathematics Kedlaya, Kiran S. Kedlaya, Kiran S. Sutherland, Andrew Victor We analyze the distribution of unitarized L-polynomials Lp(T) (as p varies) obtained from a hyperelliptic curve of genus g [less than or equal to] 3 defined over Q. In the generic case, we find experimental agreement with a predicted correspondence (based on the Katz-Sarnak random matrix model) between the distributions of Lp(T) and of characteristic polynomials of random matrices in the compact Lie group USp(2g). We then formulate an analogue of the Sato-Tate conjecture for curves of genus 2, in which the generic distribution is augmented by 22 exceptional distributions, each corresponding to a compact subgroup of USp(4). In every case, we exhibit a curve closely matching the proposed distribution, and can find no curves unaccounted for by our classification. National Science Foundation (U.S.) (NSF CAREER grant DMS-0545904) Alfred P. Sloan Foundation (Sloan Fellowship) 2011-06-29T14:44:04Z 2011-06-29T14:44:04Z 2009-01 Article http://purl.org/eprint/type/ConferencePaper 978-0-8218-4716-9 http://hdl.handle.net/1721.1/64701 Kedlaya, Kiran S. and Andrew V. Sutherland. "Hyperelliptic Curves, L-Polynomials, and Random Matrices." in Arithmetic, Geometry, Cryptography, and Coding Theory: International Conference, November 5-9, 2007, CIRM, Marseilles, France. Gilles Lachaud, Christophe Ritzenthaler, Michael A. Tsfasman, editors. 2009. (Contemporary Mathematics ; v.487) en_US http://www.ams.org/bookstore-getitem/item=CONM-487 Contemporary Mathematics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Mathematical Society Prof. Kedlaya via Michael Noga |
| spellingShingle | Kedlaya, Kiran S. Sutherland, Andrew Victor Hyperelliptic Curves, L-Polynomials, and Random Matrices |
| title | Hyperelliptic Curves, L-Polynomials, and Random Matrices |
| title_full | Hyperelliptic Curves, L-Polynomials, and Random Matrices |
| title_fullStr | Hyperelliptic Curves, L-Polynomials, and Random Matrices |
| title_full_unstemmed | Hyperelliptic Curves, L-Polynomials, and Random Matrices |
| title_short | Hyperelliptic Curves, L-Polynomials, and Random Matrices |
| title_sort | hyperelliptic curves l polynomials and random matrices |
| url | http://hdl.handle.net/1721.1/64701 |
| work_keys_str_mv | AT kedlayakirans hyperellipticcurveslpolynomialsandrandommatrices AT sutherlandandrewvictor hyperellipticcurveslpolynomialsandrandommatrices |