# 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 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.
^{ω}If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

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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