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Counter-examples to a Problem of Cohn on Classifying Characters

✍ 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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πŸ“œ SIMILAR VOLUMES


On a Character Sum Problem of Cohn
✍ PΓ€r Kurlberg πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 92 KB

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

On a Problem of H. Cohn for Character Su
✍ Todd Cochrane; David Garth; Zhiyong Zheng πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 141 KB

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