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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21665

Arratia, R; Barbour, A D; Tavaré, S (2005). A probabilistic approach to analytic arithmetic on algebraic function fields. Mathematical Proceedings of the Cambridge Philosophical Society, 139(1):1-26.

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Abstract

Knopfmacher [13] introduced the idea of an additive arithmetic semigroup as a general setting for an algebraic analogue of number theory. Within his framework, Zhang [19] showed that the asymptotic distribution of the values taken by additive functions closely resembles that found in classical number theory, in as much as there are direct analogues of the Erdos–Wintner and Kubilius Main Theorems. In this paper, we use probabilistic arguments to show that similar theorems, and their functional counterparts, can be proved in a much wider class of decomposable combinatorial structures.

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1 citation in Web of Science®
1 citation in Scopus®