Probabilistic number theory in additive arithmetic semigroups II |
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| Authors: | Wen-Bin Zhang |
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| Affiliation: | (1) Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA, US;(2) Department of Mathematics, University of The West Indies, Mona, Kingston, Jamaica (e-mail: w-zhang1@math.uiuc.edu), JM |
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| Abstract: | We prove two quantitative mean-value theorems of completely multiplicative functions on additive arithmetic semigroups. On the basis of the two theorems, a central limit theorem of additive functions on additive arithmetic semigroups is proved with a best possible error estimate. This generalizes the vital results of Halász and Elliott in classical probabilistic number theory to function fields. Received October 26, 1998; in final form April 5, 2000 / Published online October 11, 2000 |
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| Keywords: | Mathematics Subject Classification (1991): 11N60 11T55 60F05 |
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