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The computational complexity of algebraic numbers
 In ACM, editor, Conference record of Fifth Annual ACM Symposium on Theory of Computing: papers presented at the Symposium
, 1973
"... The computational complexity of algebraic numbers ..."
On the approximation to algebraic numbers by algebraic numbers
"... Abstract. Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number ε, there are infinitely many algebraic numbers α of degree at most n such that ξ − α  < H(α) −n−1+ε, where H(α) ..."
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Cited by 2 (1 self)
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Abstract. Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number ε, there are infinitely many algebraic numbers α of degree at most n such that ξ − α  < H(α) −n−1+ε, where H
Product of logarithms of algebraic numbers References
, 2005
"... Product of logarithms of algebraic numbers ..."
Algorithms in algebraic number theory
 Bull. Amer. Math. Soc
, 1992
"... Abstract. In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and, more importantly, what remains to ..."
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Cited by 53 (4 self)
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Abstract. In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and, more importantly, what remains
Algebraic Number Theory
 www.jmilne.org/math
, 2009
"... Version 3.06 May 28, 2014An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic number fields — the ring of integers in the number field, the ideals and units in the ring of int ..."
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Cited by 7 (0 self)
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Version 3.06 May 28, 2014An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic number fields — the ring of integers in the number field, the ideals and units in the ring
Algebraic Number Fields
"... Algebraic numbers are the solutions of an irreducible polynomial over some ground domain. The algebraic number i (imaginary unit), for example, would be defined by the polynomial i 2 + 1. The arithmetic of algebraic number s can be viewed as a polynomial arithmetic modulo the defining polynomial. Gi ..."
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Algebraic numbers are the solutions of an irreducible polynomial over some ground domain. The algebraic number i (imaginary unit), for example, would be defined by the polynomial i 2 + 1. The arithmetic of algebraic number s can be viewed as a polynomial arithmetic modulo the defining polynomial
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.
On the binary expansions of algebraic numbers
 JOURNAL DE THÉORIE DES NOMBRES DE BORDEAUX
"... Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1’s in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D> 1, then the number #(y, N) ..."
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Cited by 26 (4 self)
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Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1’s in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D> 1, then the number #(y, N
The conjugate dimension of algebraic numbers
 Quart. J. Math
"... We find sharp upper and lower bounds for the degree of an algebraic number in terms of the Qdimension of the space spanned by its conjugates. For all but seven nonnegative integers n the largest degree of an algebraic number whose conjugates span a vector space of dimension n is equal to 2nn!. The ..."
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Cited by 4 (0 self)
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We find sharp upper and lower bounds for the degree of an algebraic number in terms of the Qdimension of the space spanned by its conjugates. For all but seven nonnegative integers n the largest degree of an algebraic number whose conjugates span a vector space of dimension n is equal to 2nn
Results 1  10
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