Riesz means of certain arithmetic functions

RIMS - 1685 On certain arithmetic functions

On certain arithmetic functions˜M (s; z 1 , z 2) associated with global fields: Analytic properties. On certain arithmetic functions˜M (s; z 1 , z 2) associated with global fields: Analytic properties.

On certain arithmetic functions involving exponential divisors

The integer d is called an exponential divisor of n = ∏r i=1 p ai i > 1 if d = ∏r i=1 p ci i , where ci|ai for every 1 ≤ i ≤ r. The integers n = ∏r i=1 p ai i ,m = ∏r i=1 p bi i > 1 having the same prime factors are called exponentially coprime if (ai, bi) = 1 for every 1 ≤ i ≤ r. In this paper we investigate asymptotic properties of certain arithmetic functions involving exponential divisors a...

Integral means of certain multivalent functions

For analytic and multivalent functions f (z) and p(z) in the open unit disk U, a subordi-nation theorem due to Littlewood (1925) which was called the integral mean is applied. Some simple examples for our results are also considered.

Integral Means of Certain Analytic Functions

We introduce the analytic functions f (z) = z + ∞ ∑ k=n+1 akz k ( n ∈ N) and p(z) = z + m ∑ s=1 bsj−s+1zsj−s+1 (j ≥ n + 1;n ∈ N) in the open unit disk U. By means of the subordination theorem of J.E. Littlewood, we shall investigate the integral means with coefficients inequalities of analytic functions f(z) and p(z). Some applications of the integral mean of f(z) are considered. 2000 Mathemati...

Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions