author: | Andreas Weiermann |
---|---|
title: | An application of results by Hardy, Ramanujan and Karamata to Ackermannian functions |
keywords: | Ackermann function, Karamata's theorem, Hardy Ramanujan methods, analytic combinatorics |
abstract: | The Ackermann function is a fascinating and well studied paradigm for a function which eventually dominates all primitive
recursive functions. By a classical result from the theory of
recursive functions it is known that the Ackermann function can be
defined by an unnested or descent recursion along the segment of
ordinals below ω^{ω} (or equivalently
along the order type of the polynomials under eventual domination). In
this article we give a fine structure analysis of such a Ackermann
type descent recursion in the case that the ordinals below
ω^{ω} are represented via a Hardy
Ramanujan style coding. This paper combines number-theoretic results
by Hardy and Ramanujan, Karamata's celebrated Tauberian theorem and
techniques from the theory of computability in a perhaps surprising
way.
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reference: | Andreas Weiermann (2003), An application of results by Hardy, Ramanujan and Karamata to Ackermannian functions , Discrete Mathematics and Theoretical Computer Science 6, pp. 133-142 |
bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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