On a Character Sum Problem of H. Cohn
نویسنده
چکیده
and equation 1.1, does it follow that f is a multiplicative character? The problem has recently received some attention. In [2], Choi and Siu proved that the converse is not true for k > 1. One of the arguments given is quite pretty, and proceeds as follows: Let λ be a linear automorphism of Fpk so that λ(1) = 1. If f satisfies 1.1 and 1.2, so does f composed with λ. Now, if f is an injective multiplicative character then the converse being true implies that f composed with λ must be an injective multiplicative character. On the other hand, a simple counting argument shows that the number of possible λ’s is greater than the number of injective characters. However, the case k = 1 remains unresolved. In [1], Biro proved that there are only finitely many functions satisfying equation 1.1 and 1.2
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