A generalization of the Hasse–Witt matrix of a hypersurface

Alan Adolphson, Steven Sperber

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The Hasse–Witt matrix of a hypersurface in Pn over a finite field of characteristic p gives essentially complete mod p information about the zeta function of the hypersurface. But if the degree d of the hypersurface is ≤n, the zeta function is trivial mod p and the Hasse–Witt matrix is zero-by-zero. We generalize a classical formula for the Hasse–Witt matrix to obtain a matrix that gives a nontrivial congruence for the zeta function for all d. We also describe the differential equations satisfied by this matrix and prove that it is generically invertible.

Original languageEnglish (US)
Pages (from-to)203-221
Number of pages19
JournalFinite Fields and their Applications
StatePublished - Sep 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.


  • Hasse–Witt matrix
  • Zeta function


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