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On a Problem of H. Cohn for Character Sums by Todd Cochrane; David Garth; Zhiyong Zheng is a Mathematics article available to read on EtoBox.

What is On a Problem of H. Cohn for Character Sums about?

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 paper we show that if for all a, b # F\*, we have (q&1) : then f is a multiplicative character of F. We also prove that if F is a prime field and f is a real valued function on F with f (0)=0, f (1)=1, and | f (:)| =1 for all :{0, then : # F f (:) f (:+a)=&1 for all a{0 if and only if f is the Legendre symbol. These results partially answer Cohn's problem.

Who reads On a Problem of H. Cohn for Character Sums?

Author

Todd Cochrane; David Garth; Zhiyong Zheng

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-314X)

Published

2000

Language

EN

Field

Mathematics (Physical Sciences)