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Character Sums, Primitive Elements, and Powers in Finite Fields

✍ Scribed by Arne Winterhof

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
148 KB
Volume
91
Category
Article
ISSN
0022-314X

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✦ Synopsis

Consider an extension field F q m =F q (a) of the finite field F q . Davenport proved that the set F q +a contains at least one primitive element of F q m if q is sufficiently large with respect to m. This result is extended to certain subsets of F q +a of cardinality at least of the order of magnitude O(q 1/2+e ). The proof is based on a new bound for incomplete character sums. Moreover, a new bound for the longest sequence of consecutive powers in F q m is deduced.

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