Some Normal Numbers Generated by Arithmetic Functions

Some classes of statistically convergent sequences of fuzzy numbers generated by a modulus function

The purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $Delta$ and give some inclusion relations.

Arithmetic Height Functions over Finitely Generated Fields

In this paper, we propose a new height function for a variety defined over a finitely generated field overQ. For this height function, we will prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s conjecture). CONTENTS Introduction 1 1. Arakelov intersection theory 3 2. Arithmetically positive hermitian line bundles 6 3. Ari...

Normality of numbers generated by the values of entire functions

as N → ∞, where the supremum is taken over all blocks d1 . . . dl ∈ {0, 1, . . . , q − 1} . We want to look at numbers whose digits are generated by the integer part of entire functions. Let f be any function and [f(n)]q denote the base q expansion of the integer part of f(n), then define θq = θq(f) = 0.[f(1)]q[f(2)]q[f(3)]q[f(4)]q[f(5)]q[f(6)]q . . . , τq = τq(f) = 0.[f(2)]q[f(3)]q[f(5)]q[f(7)...

On the Normal Order of Arithmetic Functions.

On the Iterates of Some Arithmetic Functions

1. Introduction. For any arithmetic function f(n), we denote its iterates as follows : f l (n) = f (n) , fk (n) = fl[ fk_1(n) ] (k > 1). Let a(n) and a* (n) denote,'respectívely, the sum of the divisors of n, and the sum of its unitary divisors, where we recall that d is called a unitary divisor of n if (d,n/d) = 1. Makowski and Schinzel [3] proved that and conjectured that ak (n) lim inf n < o...