Functions of slow increase and integer sequences.
Jakimczuk, Rafael (2010)
Journal of Integer Sequences [electronic only]
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Jakimczuk, Rafael (2010)
Journal of Integer Sequences [electronic only]
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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).
Carsten Elsner, Takao Komatsu, Iekata Shiokawa (2007)
Journal de Théorie des Nombres de Bordeaux
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We compute upper and lower bounds for the approximation of hyperbolic functions at points by rationals , such that satisfy a quadratic equation. For instance, all positive integers with solving the Pythagorean equation satisfy Conversely, for every there are infinitely many coprime integers , such that and hold simultaneously for some integer . A generalization to the approximation of for rational...
Karin Halupczok (2009)
Journal de Théorie des Nombres de Bordeaux
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For and any sufficiently large odd we show that for almost all there exists a representation with primes mod for almost all admissible triplets of reduced residues mod .
Csaba Sándor (2007)
Journal de Théorie des Nombres de Bordeaux
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A slight modification of the proof of Szemerédi’s cube lemma gives that if a set satisfies , then must contain a non-degenerate Hilbert cube of dimension . In this paper we prove that in a random set determined by for , the maximal dimension of non-degenerate Hilbert cubes is a.e. nearly and determine the threshold function for a non-degenerate -cube.
Soulé, Christophe (2003)
Documenta Mathematica
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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 .