A Reverse Problem on Arithmetic Functions

A Note on Rational Arithmetic Functions

Nonstandard arithmetic and reverse mathematics

We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [HKK1984] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles ...

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...

Reflections on Symmetric Polynomials and Arithmetic Functions

Abstract. In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and power sum symmetric polynomials. We investigate properties of these families and focus on constructing their rational roots under a product induce...

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.