The number of solutions of some equations in a finite field

L. CARLITZ

doi:10.2969/jmsj/00730209

L. CARLITZ

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JOURNAL FREE ACCESS

1955 Volume 7 Issue 3 Pages 209-223

DOI https://doi.org/10.2969/jmsj/00730209

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Published: 1955 Received: December 25, 1953 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) L. Carlitz, The number of solutions of some special equations in a finite field, Pacific Journal of Mathematics, vol. 4 (1954), pp. 207-217
2) L. Carlitz, Pairs of quadratic equations in a finite field, American Journal of Mathematics, vol. 76 (1954), pp. 137-154.
3) L. Carlitz, Some special equations in a finite field, Pacific Journal of Mathemtics, vol. 3 (1953), pp. 13-24.
4) H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewißen zyklischen Fällen; Journal für die reine and angewandte Mathematik, vol. 172 (1935), pp. 151-182.
5) E. Jacobsthal, Über die Darstellung der Primzahlen der Form 4n+1 als Summe zweier Quadrate, Journal für die reine und angewandte Mathematik, vol. 132 (1907). pp. 238-245.
6) R. G. Pohrer, On the solution of equations in a finite field, not yet published.
7) A. L. Whiteman. Cyclotomy and Jacobsthal sums, American Journal of Mathematics, vol. 74 (1952), pp. 89-99.
8) A. L. Whiteman, Theorems analogous to Jacobsthal's theorem, Duke Mathematical Journal, vol. 16 (1949), pp. 619-626.

Right : 1) To find the number of solutions of such simultaneous equations in a finite field is also of interest in connection with the algebraic geometry, as was pointed out by A. Weil: Bull. Amer. Math. Soc. 55 (1949) pp. 497-508.
[1] L. Carlitz, The number of solutions of some special equations in a finite field, Pacific Journal of Mathematics, vol. 4 (1954), pp. 207-217
[2] L. Carlitz, Pairs of quadratic equations in a finite field, American Journal of Mathematics, vol. 76 (1954), pp. 137-154.
[3] L. Carlitz, Some special equations in a finite field, Pacific Journal of Mathemtics, vol. 3 (1953), pp. 13-24.
[4] H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewißen zyklischen Fällen, Journal für die reine und angewandte Mathematik, vol. 172 (1935), pp. 151-182.
[5] E. Jacobsthal, Über die Darstellung der Primzahlen der Form 4n+1 als Summe zweier Quadrate, Journal für die reine und angewandte Mathematik, vol. 132 (1907). pp. 238-245.
[6] R. G. Pohrer, On the solution of equations in a finite field, not yet published.
[7] A. L. Whiteman. Cyclotomy and Jacobsthal sums, American Journal of Mathematics, vol. 74 (1952), pp. 89-99.
[8] A. L. Whiteman, Theorems analogous to Jacobsthal's theorem, Duke Mathematical Journal, vol. 16 (1949), pp. 619-626.

Date of correction: August 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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