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A probabilistic approach to analytic arithmetic on algebraic function fields

Published online by Cambridge University Press:  22 June 2005

RICHARD ARRATIA ,
A. D. BARBOUR  and
SIMON TAVARÉ
RICHARD ARRATIA
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, U.S.A.
A. D. BARBOUR
Affiliation:
Abteilung für Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland.
SIMON TAVARÉ
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, U.S.A.
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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 Erdős–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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 1 , July 2005 , pp. 1 - 26
Copyright
2005 Cambridge Philosophical Society

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