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Annali di Matematica Pura ed Applicata

, Volume 71, Issue 1, pp 93–99 | Cite as

Representations by bilinear forms (and.p a)

  • John H. Hodges
Article

Summary

An expression is derived for the number of representations of one bilinear form by another (mod pa). From this, an explicit formula for the number of such representations is obtained in the case where both forms have square nonsingular matrices (mod p). A related bilinear analog of a lemma of Siegel on representations by quadratic forms (mod pa) is also proved.

Keywords

Quadratic Form Bilinear Form Explicit Formula Nonsingular Matrice Bilinear Analog 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    J. H. Hodges,Representations by bilinear forms in a finite field, Duke Math. J. 22 (1955), 497–510.CrossRefzbMATHMathSciNetGoogle Scholar
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    J. H. Hodges,Some matrix equations over a finite field, Annali di Matematica (IV) 44 (1957), 245–250.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    G. Landsberg,Über eine Anzahlbestimmung und eine damit zusammenhängende Reihe, J. reine. angew. Math. 111 (1898), 87–88.Google Scholar
  4. [4]
    C. C. MacDuffee,The Theory of Matrices, New York, 1946.Google Scholar
  5. [5]
    C. L. Siegel,Uber die analytische Theorie der quadratischen Formen, Ann. of Math. (2) 36 (1935), 527–606.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1966

Authors and Affiliations

  • John H. Hodges
    • 1
  1. 1.BoulderU.S.A.

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