Skip to main content
Log in

The Jacobi sums of orders thirteen and sixty and related quadratic decompositions

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Baumert, L. D., Fredricksen, H.: The cyclotomic numbers of order eighteen with applications to difference sets. Math. Comput.21, 204–219 (1967).

    Google Scholar 

  2. Cohn, H.: A second course in number theory. New York-London: John Wiley & Sons 1962.

    Google Scholar 

  3. Davenport, H., Hasse, H.: Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. Reine Angew. Math.172, 151–182 (1934).

    Google Scholar 

  4. Dickson, L. E.: Cyclotomy, higher congruences, and Waring's problem. Amer. J. Math.57, 391–424 (1935).

    Google Scholar 

  5. — Cyclotomy and trinomial congruences. Trans. Amer. Math. Soc.37, 363–380 (1935).

    Google Scholar 

  6. — Cyclotomy whene is composite. Trans. Amer. Math. Soc.38, 187–200 (1935).

    Google Scholar 

  7. Hasse, H.: Der 2n-te Potenzcharakter von 2 im Körper der 2n-ten Einheitswurzeln. Rend. Circ. Mat. Palermo, Serie II7, 185–243 (1958).

    Google Scholar 

  8. Jacobi, C. G. J.: Gesammelte Werke, Bd. 6, S. 254–274. Berlin: Reimer 1891.

    Google Scholar 

  9. Lehmer, E.: On the number of solutions ofu k+Dw 2 (modp). Pacific J. Math.5, 103–118 (1955).

    Google Scholar 

  10. Muskat, J. B.: The cyclotomic numbers of order fourteen. Acta Arithmetica11, 263–279 (1966).

    Google Scholar 

  11. — On Jacobi sums of certain composite orders. Trans. Amer. Math. Soc.134, 483–502 (1968).

    Google Scholar 

  12. Muskat, J. B., Whiteman, A. L.: The cyclotomic numbers of order twenty. Acta Arithmetica (to appear).

  13. Whiteman, A. L.: The cyclotomic numbers of order sixteen. Trans. Amer. Math. Soc.86, 401–413 (1957).

    Google Scholar 

  14. — The cyclotomic numbers of order ten. Proc. Sympos. Appl. Math.10, 95–111, Providence, R. I.: Amer. Math. Soc. 1960.

    Google Scholar 

  15. — The cyclotomic numbers of order twelve. Acta Arithmetica6, 53–76 (1960).

    Google Scholar 

  16. Zee, Y.C.: Analysis of Jacobi sums of various orders. Doctoral Dissertation, University of Pittsburgh, 1968.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zee, YC. The Jacobi sums of orders thirteen and sixty and related quadratic decompositions. Math Z 115, 259–272 (1970). https://doi.org/10.1007/BF01129976

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01129976

Keywords

Navigation