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SQUARE FORM FACTORIZATION
, 2007
"... We present a detailed analysis of SQUFOF, Daniel Shanks’ Square Form Factorization algorithm. We give the average time and space requirements for SQUFOF. We analyze the effect of multipliers, either used for a single factorization or when racing the algorithm in parallel. ..."
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We present a detailed analysis of SQUFOF, Daniel Shanks’ Square Form Factorization algorithm. We give the average time and space requirements for SQUFOF. We analyze the effect of multipliers, either used for a single factorization or when racing the algorithm in parallel.
RELATIVE GALOIS MODULE STRUCTURE OF RINGS OF INTEGERS OF ABSOLUTELY ABELIAN NUMBER FIELDS
, 2006
"... Abstract. An extension L/K of absolutely abelian number fields is said to be Leopoldt if the ring of integers OL of L is free as a module over the associated order A L/K of L/K. Furthermore, an abelian number field K is said to be Leopoldt if every extension L/K with L/Q abelian is Leopoldt. In this ..."
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Abstract. An extension L/K of absolutely abelian number fields is said to be Leopoldt if the ring of integers OL of L is free as a module over the associated order A L/K of L/K. Furthermore, an abelian number field K is said to be Leopoldt if every extension L/K with L/Q abelian is Leopoldt. In this paper, we build upon the work of many others and use explicit techniques to make progress towards a classification of Leopoldt number fields and extensions. 1.
Counting commensurability classes of hyperbolic manifolds, http://front.math.ucdavis.edu/1401.8003
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LubinTate Formal Groups and Local Class Field Theory Submitted
, 2006
"... The goal of local class field theory is to classify abelian Galois extensions of a local field K. Several definitions of local fields are in use. In this thesis, local fields, which will be defined explicitly in Section 2, are fields that are complete with respect to a discrete valuation and have a ..."
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The goal of local class field theory is to classify abelian Galois extensions of a local field K. Several definitions of local fields are in use. In this thesis, local fields, which will be defined explicitly in Section 2, are fields that are complete with respect to a discrete valuation and have a finite residue field. A prototypical first example is Qp, the completion of Q with
Algebraic number theory
"... These are notes I wrote up from my study of algebraic number theory and class field theory. ..."
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These are notes I wrote up from my study of algebraic number theory and class field theory.