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Elementary proofs of the abstract prime number theorem for algebraic function fields


Author: Wen-Bin Zhang
Journal: Trans. Amer. Math. Soc. 332 (1992), 923-937
MSC: Primary 11N80; Secondary 11M45, 11R44, 11R58
DOI: https://doi.org/10.1090/S0002-9947-1992-1061781-X
MathSciNet review: 1061781
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Abstract: Elementary proofs of the abstract prime number theorem of the form $ \Lambda (m) = {q^m} + O({q^m}{m^{ - 1}})$ for algebraic function fields are given. The proofs use a refinement of a tauberian theorem of Bombieri.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1061781-X
Keywords: Abstract prime number theorem, additive arithmetic semi-group, additive convolution, tauberian theorem
Article copyright: © Copyright 1992 American Mathematical Society

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