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 Β₯ F f(x) f(x+h)=-1 for h ] 0. We prove that this is the case for finite fields of prime cardinality u
β¦ LIBER β¦
Counter-examples to a Problem of Cohn on Classifying Characters
β Scribed by Kwok-Kwong Choi; Man-Keung Siu
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 119 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0022-314X
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Cohn's problem on character sums (see , p. 202) asks whether a multiplicative character on a finite field can be characterized by a kind of two level autocorrelation property. Let f be a map from a finite field F to the complex plane such that f (0)=0, f (1)=1, and | f (:)| =1 for all :{0. In this p
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