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

Zhang, Wen-Bin

doi:10.1090/S0002-9947-1992-1061781-X

Elementary proofs of the abstract prime number theorem for algebraic function fields
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Trans. Amer. Math. Soc. 332 (1992), 923-937 Request permission

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

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Correction to my paper "Sull’analogo della formula di Selberg nei corpi di funzioni"

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On a tauberian theorem connected with the new proof of the prime number theorem

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