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A probabilistic approach to analytic arithmetic on algebraic function fields


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.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2005
Deposited On:02 Feb 2010 11:16
Last Modified:05 Apr 2016 13:24
Publisher:Cambridge University Press
ISSN:0305-0041
Additional Information:Copyright © 2005 Cambridge Philosophical Society
Publisher DOI:10.1017/S0305004105008583
Permanent URL: http://doi.org/10.5167/uzh-21665

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