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The Weil height in terms of an auxiliary polynomial
 Acta Arith
"... Abstract. Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number α under certain assumptions on α. We prove a theorem which introduces an auxiliary polynomial for giving lower bounds on the height of any algebraic number. ..."
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Cited by 3 (2 self)
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Abstract. Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number α under certain assumptions on α. We prove a theorem which introduces an auxiliary polynomial for giving lower bounds on the height of any algebraic number
A Banach space determined by the Weil height
 Acta Arith
"... Abstract. The absolute logarithmic Weil height is well defined on the quotient group Q × /Tor ` Q ×´ and induces a metric topology in this group. We show that the completion of this metric space is a Banach space over the field R of real numbers. We further show that this Banach space is isometrical ..."
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Cited by 7 (1 self)
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Abstract. The absolute logarithmic Weil height is well defined on the quotient group Q × /Tor ` Q ×´ and induces a metric topology in this group. We show that the completion of this metric space is a Banach space over the field R of real numbers. We further show that this Banach space
Algebraic Numbers of Small Weil’s height in CMfields: on a Theorem of Schinzel ∗
, 2009
"... Let K be a CMfield. A. Schinzel proved ([Sch 1973]) that the Weil height of nonzero algebraic numbers in K is bounded from below by an absolute constant C outside the set of algebraic numbers such that α  = 1 (since ..."
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Cited by 5 (1 self)
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Let K be a CMfield. A. Schinzel proved ([Sch 1973]) that the Weil height of nonzero algebraic numbers in K is bounded from below by an absolute constant C outside the set of algebraic numbers such that α  = 1 (since
ESTIMATING HEIGHTS USING AUXILIARY FUNCTIONS
"... Abstract. Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to problems involving the Weil height. The height appears as ..."
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Cited by 1 (0 self)
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Abstract. Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to problems involving the Weil height. The height appears
The Height in Terms of the Normalizer of a Stabilizer
, 2008
"... This dissertation is about the Weil height of algebraic numbers and the Mahler measure of polynomials in one variable. We investigate connections between the normalizer of a stabilizer and lower bounds for the Weil height of algebraic numbers. In the archimedean case we extend a result of Schinzel [ ..."
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This dissertation is about the Weil height of algebraic numbers and the Mahler measure of polynomials in one variable. We investigate connections between the normalizer of a stabilizer and lower bounds for the Weil height of algebraic numbers. In the archimedean case we extend a result of Schinzel
Points of bounded height on del Pezzo surfaces
 Compositio Math
, 1993
"... 0.1. Heights. In this paper, we prove some results on the asymptotic behaviour of the number of algebraic points of bounded height on del Pezzo (and more general) rational surfaces. The basic (Weil) height on a coordinatized projective space over an algebraic number field k is given by the formula ..."
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Cited by 8 (2 self)
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0.1. Heights. In this paper, we prove some results on the asymptotic behaviour of the number of algebraic points of bounded height on del Pezzo (and more general) rational surfaces. The basic (Weil) height on a coordinatized projective space over an algebraic number field k is given by the formula
RIGID LATTICES ARE MORDELLWEIL
, 2004
"... Abstract. We say a lattice Λ is rigid if it its isometry group acts irreducibly on its ambient Euclidean space. We say Λ is MordellWeil if there exists an abelian variety A over a number field K such that A(K)/A(K)tor, regarded as a lattice by means of its height pairing, contains at least one copy ..."
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Abstract. We say a lattice Λ is rigid if it its isometry group acts irreducibly on its ambient Euclidean space. We say Λ is MordellWeil if there exists an abelian variety A over a number field K such that A(K)/A(K)tor, regarded as a lattice by means of its height pairing, contains at least one
bounds on the projective heights of algebraic points
 Acta Arith
"... Abstract. If α1,..., αr are algebraic numbers such that r ∑ r∑ N = i=1 αi ̸= i=1 α −1 i for some integer N, then a theorem of Beukers and Zagier [1] gives the best possible lower bound on r∑ log h(αi) i=1 where h denotes the Weil Height. We will extend this result to allow N to be any totally real a ..."
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Cited by 4 (1 self)
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Abstract. If α1,..., αr are algebraic numbers such that r ∑ r∑ N = i=1 αi ̸= i=1 α −1 i for some integer N, then a theorem of Beukers and Zagier [1] gives the best possible lower bound on r∑ log h(αi) i=1 where h denotes the Weil Height. We will extend this result to allow N to be any totally real
Heights On Elliptic Curves And The Diophantine Equation
, 1998
"... . In this paper we give sharp explicit estimates for the difference of the Weil height and the N'eron  Tate height on the elliptic curve v 2 = u 3 \Gamma cu. We then apply this in the proof of the fact that if c ? 2 is a fourth power free integer and the rank of v 2 = u 3 \Gamma cu is ..."
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. In this paper we give sharp explicit estimates for the difference of the Weil height and the N'eron  Tate height on the elliptic curve v 2 = u 3 \Gamma cu. We then apply this in the proof of the fact that if c ? 2 is a fourth power free integer and the rank of v 2 = u 3 \Gamma cu
Integral points of fixed degree and bounded height. preprint
"... In this article we count algebraic points of bounded Weil height with integral coordinates, generating an extension of given degree over a fixed number field k. We derive a precise asymptotic formula for their number as the height gets large. Various related results have appeared in the literature. ..."
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Cited by 3 (2 self)
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In this article we count algebraic points of bounded Weil height with integral coordinates, generating an extension of given degree over a fixed number field k. We derive a precise asymptotic formula for their number as the height gets large. Various related results have appeared in the literature
Results 1  10
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