Discrete Mathematics & Theoretical Computer Science
| 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.
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. |
| ps.gz-source: | dm060111.ps.gz (51 K) |
| ps-source: | dm060111.ps (131 K) |
| pdf-source: | dm060111.pdf (89 K) |
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