Some Numerical Results on Fekete Polynomials
نویسندگان
چکیده
It is known that if x is a real residue character modulo k with x(p) = — 1 k n for the first five primes p, then the corresponding Fekete polynomial £„=j X(n)x changes sign on (0, 1). In this paper it is shown that the condition that x(p) be — 1 for the first four primes p is not sufficient to guarantee such a sign change. More specifically, if x ¡s the real nonprincipal character modulo either 1277 or 1973, it is shown that the corresponding Fekete polynomial is positive throughout (0, 1) even though X(2) = X(3) = x(5) = x(7) = 1.
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