Discrete Mathematics & Theoretical Computer Science


Volume 6 n° 1 (2003), pp. 133-142

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 ωω (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 ωω 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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