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» The Number Field Sieve
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90
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EM
2010
124views Management» more  EM 2010»
14 years 8 months ago
On the Distribution of Class Groups of Number Fields
We propose a modification of the predictions of the Cohen
Gunter Malle
ANTS
2008
Springer
83views Algorithms» more  ANTS 2008»
15 years 3 months ago
Enumeration of Totally Real Number Fields of Bounded Root Discriminant
We enumerate all totally real number fields F with root discriminant F 14. There are 1229 such fields, each with degree [F : Q] 9. In this article, we consider the following prob...
John Voight
104
Voted
ANTS
1998
Springer
139views Algorithms» more  ANTS 1998»
15 years 6 months ago
Generating Arithmetically Equivalent Number Fields with Elliptic Curves
In this note we address the question whether for a given prime number p, the zeta-function of a number field always determines the p-part of its class number. The answer is known t...
Bart de Smit
ANTS
2004
Springer
111views Algorithms» more  ANTS 2004»
15 years 7 months ago
A Method to Solve Cyclotomic Norm Equations
We present a technique to recover f ∈ Q(ζp) where ζp is a primitive pth root of unity for a prime p, given its norm g = f ∗ ¯f in the totally real field Q(ζp + ζ−1 p )....
Nick Howgrave-Graham, Michael Szydlo
MOC
2000
71views more  MOC 2000»
15 years 1 months ago
Zeroes of Dirichlet L-functions and irregularities in the distribution of primes
Seven widely spaced regions of integers with 4,3(x) < 4,1(x) have been discovered using conventional prime sieves. Assuming the generalized Riemann hypothesis, we modify a resul...
Carter Bays, Richard H. Hudson