A-hypergeometric series and a p-adic refinement of the Hasse-Witt matrix

Alan Adolphson, Steven Sperber

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We identify the p-adic unit roots of the zeta function of a projective hypersurface over a finite field of characteristic p as the eigenvalues of a product of special values of a certain matrix of p-adic series. That matrix is a product F(Λp)-1F(Λ), where the entries in the matrix F(Λ) are A-hypergeometric series with integral coefficients and F(Λ) is independent of p.

Original languageEnglish (US)
Pages (from-to)225-256
Number of pages32
JournalAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Issue number2
StateAccepted/In press - 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg.


  • A-hypergeometric series
  • Hasse-Witt matrix
  • p-adic cohomology


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