The Chebotarev Density Theorem in Short Intervals and Some Questions of Serre
نویسندگان
چکیده
the unique normalized cusp form of weight 12 with respect to the full modular group. Although Lehmer’s speculation that τ(n) 6= 0 for every positive n remains open, Serre [S] has made substantial progress on the basic question regarding the number of Fourier coefficients of a modular form which can be zero. He shows (see [p. 179, S]) that τ(n) is non-zero for the vast majority of n. In the same paper, Serre proposes the study of the nonvanishing of Fourier coefficients in short intervals. In particular, if
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