Hyperelliptic Curves, L-Polynomials, and Random Matrices
Name
Kedlaya Hyperelliptic Curves....pdf
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1.34 MB
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Author(s)
Kedlaya, Kiran S.
Sutherland, Andrew Victor
Date Issued
January 2009
Journal
Contemporary Mathematics
Publisher
American Mathematical Society
Citation
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)
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
http://www.ams.org/bookstore-getitem/item=CONM-487
