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math.NTJan 1, 2008
33
citations (OpenAlex)
authors
  • Kiran S. Kedlaya
  • Andrew V. Sutherland
institutions
  • Massachusetts Institute of Technology
arXiv abstractPDF
paper

Computing L-series of hyperelliptic curves

arXiv:0801.2778 · doi:10.1007/978-3-540-79456-1_21

Abstract

We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic methods.

15 pages, corrected minor typos

Cited by in corpus (13)

  • Sato-Tate distributions and Galois endomorphism modules in genus 2
  • A database of genus 2 curves over the rational numbers
  • Computing images of Galois representations attached to elliptic curves
  • Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time
  • Sato-Tate distributions of twists of y^2=x^5-x and y^2=x^6+1
  • A database of nonhyperelliptic genus 3 curves over Q
  • Computing L-series of geometrically hyperelliptic curves of genus three
  • Elliptic aliquot cycles of fixed length
  • Fast Jacobian arithmetic for hyperelliptic curves of genus 3
  • Counting points on genus-3 hyperelliptic curves with explicit real multiplication
  • Computing L-Polynomials of Picard curves from Cartier-Manin matrices
  • Counting points on smooth plane quartics
  • Computing Euler factors of genus 2 curves at odd primes of almost good reduction
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