Displaying similar documents to “Lower bounds for a certain class of error functions”

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).

Sign changes of error terms related to arithmetical functions

Paulo J. Almeida (2007)

Journal de Théorie des Nombres de Bordeaux

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Let H ( x ) = n x φ ( n ) n - 6 π 2 x . Motivated by a conjecture of Erdös, Lau developed a new method and proved that # { n T : H ( n ) H ( n + 1 ) &lt; 0 } T . We consider arithmetical functions f ( n ) = d n b d d whose summation can be expressed as n x f ( n ) = α x + P ( log ( x ) ) + E ( x ) , where P ( x ) is a polynomial, E ( x ) = - n y ( x ) b n n ψ x n + o ( 1 ) and ψ ( x ) = x - x - 1 / 2 . We generalize Lau’s method and prove results about the number of sign changes for these error terms.