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On a Character Sum Problem of Cohn

✍ Scribed by Pär Kurlberg

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
92 KB
Volume
92
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let f be a complex-valued function on a finite field F such that f(0)=0, f(1)=1, and |f(x)|=1 for x ] 0. H. Cohn asked if it follows that f is a nontrivial multiplicative character provided that ; x ¥ F f(x) f(x+h)=-1 for h ] 0. We prove that this is the case for finite fields of prime cardinality under the assumption that the nonzero values of f are roots of unity.

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