A constant in pluripotential theory
Zbigniew Błocki (1992)
Annales Polonici Mathematici
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We compute the constant sup : P a polynomial in , where S denotes the euclidean unit sphere in and σ its unitary surface measure.
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Zbigniew Błocki (1992)
Annales Polonici Mathematici
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We compute the constant sup : P a polynomial in , where S denotes the euclidean unit sphere in and σ its unitary surface measure.
Florian Luca, Paul Pollack (2011)
Journal de Théorie des Nombres de Bordeaux
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Let denote Euler’s totient function. A century-old conjecture of Carmichael asserts that for every , the equation has a solution . This suggests defining as the number of solutions to the equation . (So Carmichael’s conjecture asserts that always.) Results on are scattered throughout the literature. For example, Sierpiński conjectured, and Ford proved, that the range of contains every natural number . Also, the maximal order of has been investigated by Erdős and Pomerance....
Nicolas Gouillon (2006)
Journal de Théorie des Nombres de Bordeaux
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We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in []. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around instead of .
G. S. Srivastava, Sunita Rani (1992)
Annales Polonici Mathematici
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Let f(z), , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values and the iterated mean values of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).
Soulé, Christophe (2003)
Documenta Mathematica
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Alain Togbé (2006)
Journal de Théorie des Nombres de Bordeaux
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In this paper, we use Baker’s method, based on linear forms of logarithms, to solve a family of Thue equations associated with a family of number fields of degree 3. We obtain all solutions to the Thue equation for .