Displaying similar documents to “Functions of slow increase and integer sequences.”

On the mean values of an analytic function.

G. S. Srivastava, Sunita Rani (1992)

Annales Polonici Mathematici

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Let f(z), z = r e i θ , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values I δ ( r ) and the iterated mean values N δ , k ( r ) 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).

A constant in pluripotential theory

Zbigniew Błocki (1992)

Annales Polonici Mathematici

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We compute the constant sup ( 1 / d e g P ) ( m a x S l o g | P | - ∫ S l o g | P | d σ ) : P a polynomial in ℂ n , where S denotes the euclidean unit sphere in ℂ n and σ its unitary surface measure.

Approximation of values of hypergeometric functions by restricted rationals

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 1 / s ( s = 1 , 2 , ⋯ ) by rationals x / y , such that x , y satisfy a quadratic equation. For instance, all positive integers x , y with y ≡ 0 ( mod 2 ) solving the Pythagorean equation x 2 + y 2 = z 2 satisfy | y sinh ( 1 / s ) - x | ≫ log log y log y . Conversely, for every s = 1 , 2 , ⋯ there are infinitely many coprime integers x , y , such that | y sinh ( 1 / s ) - x | ≪ log log y log y and x 2 + y 2 = z 2 hold simultaneously for some integer z . A generalization to the approximation of h ( e 1 / s ) for rational...