On the Coefficients of the Cyclotomic Polynomial
نویسنده
چکیده
For n<105 all coefficients of Fn(x) are ±1 or 0. For n = 10S, the coefficient 2 occurs for the first time. Denote by A w the greatest coefficient of Fn(x) (in absolute value). Schur proved that lim sup -4n= °°. Emma Lehmer proved that An>cn l,z for infinitely many n. In fact she proved that infinitely many such w's are of the form pqr with p, q, and r prime. In the present note we are going to prove that An>n k for every k and infinitely many n. This is implied by the still sharper theorem: THEOREM I. For infinitely many n An > exp [*i(log w) ].
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