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ANTS
2006
Springer
118views Algorithms» more  ANTS 2006»
11 years 7 months ago
Construction of Rational Points on Elliptic Curves over Finite Fields
Abstract. We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the...
Andrew Shallue, Christiaan van de Woestijne
ANTS
2006
Springer
75views Algorithms» more  ANTS 2006»
11 years 7 months ago
Symmetric Powers of Elliptic Curve L-Functions
Abstract. The conjectures of Deligne, Beilinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of t...
Phil Martin, Mark Watkins
ANTS
2006
Springer
122views Algorithms» more  ANTS 2006»
11 years 7 months ago
The Mertens Conjecture Revisited
Tadej Kotnik, Herman te Riele
ANTS
2006
Springer
132views Algorithms» more  ANTS 2006»
11 years 9 months ago
20 Years of ECM
Paul Zimmermann, Bruce Dodson
ANTS
2006
Springer
105views Algorithms» more  ANTS 2006»
11 years 9 months ago
A Modular Method for Computing the Splitting Field of a Polynomial
We provide a modular method for computing the splitting field Kf of an integral polynomial f by suitable use of the byproduct of computation of its Galois group Gf by p-adic Staudu...
Guénaël Renault, Kazuhiro Yokoyama
ANTS
2006
Springer
114views Algorithms» more  ANTS 2006»
11 years 9 months ago
The Pseudosquares Prime Sieve
We present the pseudosquares prime sieve, which finds all primes up to n. Define p to be the smallest prime such that the pseudosquare Lp > n/((p)(log n)2 ); here (x) is the pri...
Jonathan Sorenson
ANTS
2006
Springer
127views Algorithms» more  ANTS 2006»
11 years 9 months ago
Doubly-Focused Enumeration of Pseudosquares and Pseudocubes
This paper offers numerical evidence for a conjecture that primality proving may be done in (log N)3+o(1) operations by examining the growth rate of quantities known as pseudosquar...
Kjell Wooding, Hugh C. Williams
ANTS
2006
Springer
105views Algorithms» more  ANTS 2006»
11 years 9 months ago
Determined Sequences, Continued Fractions, and Hyperelliptic Curves
In this report I sanitise (in the sense of `bring some sanity to') the arguments of earlier reports detailing the correspondence between sequences (M +hS)-<h< of divisor...
Alfred J. van der Poorten
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