Hyperelliptic curves, L-polynomials, and random matrices

@article{Kedlaya2008HyperellipticCL,
  title={Hyperelliptic curves, L-polynomials, and random matrices},
  author={K. Kedlaya and Andrew V. Sutherland},
  journal={arXiv: Number Theory},
  year={2008}
}
We analyze the distribution of unitarized L-polynomials Lp(T) (as p varies) obtained from a hyperelliptic curve of genus g <= 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… Expand
29 Citations
Moments of zeta functions associated to hyperelliptic curves over finite fields
  • M. Rubinstein, Kaiyu Wu
  • Mathematics, Medicine
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2015
  • 16
  • Highly Influenced
  • PDF
Computing -series of geometrically hyperelliptic curves of genus three
  • 11
  • PDF
Sato-Tate groups of genus 2 curves
  • K. Kedlaya
  • Mathematics, Computer Science
  • Advances on Superelliptic Curves and their Applications
  • 2015
  • 5
  • PDF
Genus Two Curves with Many Elliptic Subcovers
  • 3
Sato-Tate Distributions
  • 11
  • PDF
...
1
2
3
...

References

SHOWING 1-10 OF 74 REFERENCES
...
1
2
3
4
5
...