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Notes on a Problem of H. Cohn

✍ Scribed by András Biró

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
103 KB
Volume
77
Category
Article
ISSN
0022-314X

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✦ Synopsis

We prove some partial results concerning the following problem: Assume that F is a finite field, a i is a complex number for each i # F such that a 0 =0, a 1 =1, |a i | =1 for all i # F "[0], and i # F a i+j aÄ i =&1 for all i # F "[0]. Does it follow that the function i Ä a i is a multiplicative character of F ? We prove (in the case |F | =p, p is a prime) on the one hand that there is only a finite number of complex solutions; on the other hand we solve completely a mod p version of the problem. The proofs are mainly elementary, except for applying a theorem of Chevalley from algebraic geometry.

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