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Vanishing Sums ofmth Roots of Unity in Finite Fields

✍ Scribed by T.Y. Lam; K.H. Leung

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
273 KB
Volume
2
Category
Article
ISSN
1071-5797

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✦ Synopsis

In an earlier work, the authors determined all possible weights n for which there exists a vanishing sum 1 Ο© ΠΈ ΠΈ ΠΈ Ο© n Ο­ 0 of mth roots of unity i in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic p. For given m and p, results are obtained on integers n 0 such that all integers n Υ† n 0 are in the ''weight set'' W p (m). The main result in this paper guarantees, under suitable conditions, the existence of solutions of x d 1 Ο© ΠΈ ΠΈ ΠΈ Ο© x d n Ο­ 0 with all coordinates not equal to zero over a finite field.

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