On additive arithmetic functions f(n) for which f(an + b) − f(cn + d) is bounded

(i) Additive Arithmetic Functions Bounded by Monotone Functions on Thin Sets

1 . An arithmetic function f(n) is said to be additive if it satisfies the relation f(ob) = f(a)+f(b) for every pair of coprime positive integers a, b . In this paper we establish two results to the effect that an additive function which is not too large on many integers cannot often be large on the primes . If a l <a,< . . . is a sequence of positive integers, let A(x) denote ttie number of su...

Decomposition of threshold functions into bounded fan-in threshold functions

Article history: Received 31 October 2007 Revised 3 March 2011 Available online 10 April 2013

Functional Analysis and Additive Arithmetic Functions

1. A function is arithmetic if it is defined on the positive integers. Those arithmetic functions which assume real values and satisfy f(ab)-f(a)+f(b) for mutually prime integers a, b are classically called additive. The following examples illustrate the interest of these functions, both for themselves and for their applications. An additive function is defined by its values on the prime powers...

Provably Total Functions in Bounded Arithmetic Theories . . .

Chapters on Bounded Arithmetic

We characterize the collapse of Buss’ bounded arithmetic in terms of the prov­ able collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.