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An application of results by Hardy, Ramanujan and Karamata to Ackermannian functions
Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 1.

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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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     author = {Weiermann, Andreas},
     title = {An application of results by {Hardy,} {Ramanujan} and {Karamata} to {Ackermannian} functions},
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Weiermann, Andreas. An application of results by Hardy, Ramanujan and Karamata to Ackermannian functions. Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 1. doi : 10.46298/dmtcs.339. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.339/

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