Explicit bounds and heuristics on class numbers in hyperelliptic function fields

DOI10.1090/S0025-5718-01-01385-0zbMath0992.11068MaRDI QIDQ2781230

Andreas Stein, Edlyn Teske

Publication date: 19 March 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

class numberregulatorhyperelliptic function fieldanalysis of character sumstruncated Euler product

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Class groups and Picard groups of orders (11R65) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (9)

On the size of the Jacobians of curves over finite fields ⋮ Point counting on Picard curves in large characteristic ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ l-PARTS OF DIVISOR CLASS GROUPS OF CYCLIC FUNCTION FIELDS OF DEGREE l ⋮ Robust improvement in estimation of a covariance matrix in an elliptically contoured distribution ⋮ Construction of hyperelliptic function fields of high three-rank ⋮ The parallelized Pollard kangaroo method in real quadratic function fields ⋮ A generic approach to searching for Jacobians ⋮ Cryptographic aspects of real hyperelliptic curves

Cites Work

• Algebraic function fields and codes
• Hyperelliptic cryptosystems
• On an analogue of the Sato conjecture
• The continued fraction algorithm and regulator for quadratic function fields of characteristic 2
• Key-exchange in real quadratic congruence function fields
• Lectures on the theory of algebraic functions of one variable
• The parallelized Pollard kangaroo method in real quadratic function fields
• Computation of the Class Number and Class Group of a Complex Cubic Field
• On the theory of congruence function fields
• Zeroes of zeta functions and symmetry
• Computing discrete logarithms in real quadratic congruence function fields of large genus
• Real and imaginary quadratic representations of hyperelliptic function fields
• Some Methods for Evaluating the Regulator of a Real Quadratic Function Field
• An Investigation of Bounds for the Regulator of Quadratic Fields
• How the Number of Points of An Elliptic Curve Over a Fixed Prime Field Varies
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Explicit bounds and heuristics on class numbers in hyperelliptic function fields