Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time
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Publication:2878840
DOI10.1112/S1461157014000187zbMath1296.11076arXiv1402.3246OpenAlexW3099539660MaRDI QIDQ2878840
Andrew V. Sutherland, David I. Harvey
Publication date: 5 September 2014
Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1402.3246
Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Zeta and (L)-functions in characteristic (p) (11M38)
Related Items (21)
Frobenius structures on hypergeometric equations ⋮ Computing representation matrices for the action of Frobenius on cohomology groups ⋮ On the complexity of integer matrix multiplication ⋮ Computing zeta functions of arithmetic schemes ⋮ Computing the geometric endomorphism ring of a genus-2 Jacobian ⋮ Efficient search for superspecial hyperelliptic curves of genus four with automorphism group containing \(\mathbf{C}_6\) ⋮ Sato-Tate distributions of Catalan curves ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Fast Jacobian arithmetic for hyperelliptic curves of genus 3 ⋮ A database of nonhyperelliptic genus-3 curves over \(\mathbb{Q}\) ⋮ Character theory approach to Sato–Tate groups ⋮ Sato-Tate distributions ⋮ HYPERELLIPTIC CURVES, CARTIER — MANIN MATRICES AND LEGENDRE POLYNOMIALS ⋮ Sato-Tate distributions of twists of the Fermat and the Klein quartics ⋮ Hasse–Witt and Cartier–Manin matrices: A warning and a request ⋮ Maps between curves and arithmetic obstructions ⋮ Sato-Tate distributions of \(y^2=x^p-1\) and \(y^2=x^{2p}-1\) ⋮ Counting points on superelliptic curves in average polynomial time ⋮ On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average ⋮ Counting points on smooth plane quartics ⋮ Computing 𝐿-polynomials of Picard curves from Cartier–Manin matrices
Cites Work
- Genus 2 point counting over prime fields
- A cache-friendly truncated FFT
- On the Jacobian varieties of hyperelliptic curves over fields of characteristic \(p>2\)
- Hasse-Witt matrices for the Fermat curves of prime degree
- Faster arithmetic for number-theoretic transforms
- Counting points on hyperelliptic curves in average polynomial time
- Modern Computer Algebra
- Structure computation and discrete logarithms in finite abelian $p$-groups
- Counting Points on Genus 2 Curves with Real Multiplication
- Sato–Tate distributions and Galois endomorphism modules in genus 2
- Computing L-Series of Hyperelliptic Curves
- Linear Recurrences with Polynomial Coefficients and Application to Integer Factorization and Cartier–Manin Operator
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