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ON THE ARITHMETIC–GEOMETRIC MEAN INEQUALITY
"... Abstract. We obtain some refinements of the Arithmetic–Geometric mean inequality. As an application, we find the maximum value of a multivariable function. 1. ..."
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Abstract. We obtain some refinements of the Arithmetic–Geometric mean inequality. As an application, we find the maximum value of a multivariable function. 1.
ArithmeticGeometric Means Revisited
"... We use Maple's gfun library to study the limit formulae for a twoterm recurrence (iteration) AGN , which in the case N = 2 specializes to the wellknown ArithmeticGeometric Mean iteration of Gauss. Our main aim is to independently rediscover and prove the limit formulae for two classical cases ..."
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We use Maple's gfun library to study the limit formulae for a twoterm recurrence (iteration) AGN , which in the case N = 2 specializes to the wellknown ArithmeticGeometric Mean iteration of Gauss. Our main aim is to independently rediscover and prove the limit formulae for two classical
ON INEQUALITIES FOR HYPERGEOMETRIC ANALOGUES OF THE ARITHMETICGEOMETRIC MEAN
, 2007
"... ABSTRACT. In this note, we present sharp inequalities relating hypergeometric analogues of the arithmeticgeometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmeticgeometric mean established in [10]. Key words and phrases: A ..."
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Cited by 2 (1 self)
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ABSTRACT. In this note, we present sharp inequalities relating hypergeometric analogues of the arithmeticgeometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmeticgeometric mean established in [10]. Key words and phrases
ON THE ARITHMETICGEOMETRIC MEAN FOR CURVES OF GENUS 2
, 2007
"... We study the relationship between two genus 2 curves whose jacobians are isogenous with kernel equal to a maximal isotropic subspace of ptorsion points with respect to the Weil pairing. When p = 2 this relationship is a generalization of Gauss’s arithmeticgeometric mean for elliptic curves studied ..."
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We study the relationship between two genus 2 curves whose jacobians are isogenous with kernel equal to a maximal isotropic subspace of ptorsion points with respect to the Weil pairing. When p = 2 this relationship is a generalization of Gauss’s arithmeticgeometric mean for elliptic curves
AN ALTERNATIVE AND UNITED PROOF OF A DOUBLE INEQUALITY FOR BOUNDING THE ARITHMETICGEOMETRIC MEAN
, 902
"... Abstract. In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmeticgeometric mean. 1. ..."
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Cited by 6 (6 self)
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Abstract. In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmeticgeometric mean. 1.
Formulas for the arithmetic geometric mean of curves of genus 3
, 2004
"... The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3. ..."
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Cited by 3 (2 self)
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The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3.
An explicit formula for the arithmetic geometric mean in genus 3
 EXPERIMENTAL MATH
, 2005
"... The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3. ..."
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Cited by 2 (0 self)
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The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3.
Interpolating between the ArithmeticGeometric Mean and CauchySchwarz matrix norm inequalities
"... We prove an inequality for unitarily invariant norms that interpolates between the ArithmeticGeometric Mean inequality and the CauchySchwarz inequality. Key words: eigenvalue inequality, matrix norm inequality ..."
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We prove an inequality for unitarily invariant norms that interpolates between the ArithmeticGeometric Mean inequality and the CauchySchwarz inequality. Key words: eigenvalue inequality, matrix norm inequality
Results 1  10
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81,710