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p-Adic valuations associated to fibers and images of polynomial functions.
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- Author(s): Cao, Wei1 (AUTHOR)
- Source:
Finite Fields & Their Applications. Jan2022, Vol. 77, pN.PAG-N.PAG. 1p.- Subject Terms:
- Source:
- Additional Information
- Abstract: The Chevalley-Warning and the Ax-Katz theorems, which provide the p -adic valuations for the number of solutions of the system of polynomials in finite fields, are stated in terms of the degrees of the associated polynomials. Recently, Clark et al. reformulated the theorems in terms of the cardinalities of fibers and images of the associated polynomial functions, and raised a question in this setting. In this paper, we give a negative answer to that question and improve their results in general case using p -adic lifting via the Teichmüller character. [ABSTRACT FROM AUTHOR]
- Abstract: Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Abstract:
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