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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Sets definable over finite fields: their zeta-functions


Author: Catarina Kiefe
Journal: Trans. Amer. Math. Soc. 223 (1976), 45-59
MSC: Primary 14G10; Secondary 12C25, 02H15
MathSciNet review: 0422281
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Abstract: Sets definable over finite fields are introduced. The rationality of the logarithmic derivative of their zeta-function is established, an application of purely algebraic content is given. The ingredients used are a result of Dwork on algebraic varieties over finite fields and model-theoretic tools.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0422281-1
Keywords: Finite and pseudo-finite fields, varieties, definable sets, zeta-function, elimination of quantifiers
Article copyright: © Copyright 1976 American Mathematical Society