Algorithmic Number Theory

Invited Talks.- Computing Zeta Functions via p-Adic Cohomology.- Using Primitive Subgroups to Do More with Fewer Bits.- Elliptic Curves of Large Rank and Small Conductor.- Contributed Papers.- Binary GCD Like Algorithms for Some Complex Quadratic Rings.- On the Complexity of Computing Units in a Number Field.- Implementing the Arithmetic of C 3,4 Curves.- Pseudocubes and Primality Testing.- Elliptic Curves with a Given Number of Points.- Rational Divisors in Rational Divisor Classes.- Conjectures about Discriminants of Hecke Algebras of Prime Level.- Montgomery Scalar Multiplication for Genus 2 Curves.- Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves.- Elliptic Curves x 3 + y 3 = k of High Rank.- Proving the Primality of Very Large Numbers with fastECPP.- A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii's Algorithm.- Function Field Sieve in Characteristic Three.- A Comparison of CEILIDH and XTR.- Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication.- An Algorithm for Computing Isomorphisms of Algebraic Function Fields.- A Method to Solve Cyclotomic Norm Equations .- Imaginary Cyclic Quartic Fields with Large Minus Class Numbers.- Nonic 3-adic Fields.- Montgomery Addition for Genus Two Curves.- Numerical Evaluation at Negative Integers of the Dedekind Zeta Functions of Totally Real Cubic Number Fields.- Salem Numbers of Trace -2 and Traces of Totally Positive Algebraic Integers.- Low-Dimensional Lattice Basis Reduction Revisited.- Computing Order Statistics in the Farey Sequence.- The Discrete Logarithm in Logarithmic l-Class Groups and Its Applications in K-theory.- Point Counting on Genus 3 Non Hyperelliptic Curves.- Algorithmic Aspects of Cubic Function Fields.- A Binary Recursive Gcd Algorithm.- Lagrange Resolvents Constructed from Stark Units.- Cryptanalysis of a Divisor Class Group Based Public-Key Cryptosystem.