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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 377, Pages 55–62 (Mi znsl3814)  
This article is cited in 1 scientific paper (total in 1 paper)

Non-singular points on hypersurfaces over $\mathbb F_q$

J. Zahid

University of Bristol
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Abstract: In this survey article we investigate hypersurfaces defined over finite fields. More specifically we determine for which hypersurfaces one can ensure the existence of a non-singular point taking the cardinality of our ambient field large if need be. Additionally for such hypersurfaces we will find a lower bound on the cardinality for which a non-singular point is guaranteed. Bibl. 11 titles.
Key words and phrases: non-singular points, finite fields, hypersurface, Bertini's theorem, Lang–Weil estimates.
Received: 02.06.2010
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 171, Issue 6, Pages 731–735
DOI: https://doi.org/DOI: 10.1007/s10958-010-0177-6 https://doi.org/DOI: 10.1007/s10958-010-0177-6
Document Type: Article
UDC: 512.757
Language: English
Citation: J. Zahid, “Non-singular points on hypersurfaces over $\mathbb F_q$”, Studies in number theory. Part 10, Zap. Nauchn. Sem. POMI, 377, POMI, St. Petersburg, 2010, 55–62; J. Math. Sci. (N. Y.), 171:6 (2010), 731–735
Citation in format AMSBIB
\Bibitem{Zah10}
\by J.~Zahid
\paper Non-singular points on hypersurfaces over $\mathbb F_q$
\inbook Studies in number theory. Part~10
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 377
\pages 55--62
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3814}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 171
\issue 6
\pages 731--735
\crossref{https://doi.org/DOI: 10.1007/s10958-010-0177-6}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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