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Hilbert's Tenth Problem for fields of rational functions over finite fields

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We prove that there is no algorithm to solve arbitrary polynomial equations over a field of rational functions in one letter with constants in a finite field of characteristic other than 2 and hence, Hilbert's Tenth Problem for any such field is undecidable.

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Author notes

  1. Thanases Pheidas

    Present address: Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, IL, USA

Authors and Affiliations

  1. Department of Mathematics, Florida International University, 33199, Miami, FL, USA

    Thanases Pheidas

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  1. Thanases Pheidas
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Additional information

Oblatum 1-XI-1989

Supported in part by NSF Grant DMS 8605198.

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Pheidas, T. Hilbert's Tenth Problem for fields of rational functions over finite fields. Invent Math 103, 1–8 (1991). https://doi.org/10.1007/BF01239506

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  • DOI: https://doi.org/10.1007/BF01239506

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