Oscillations of Fourier Coefficients of Modular Forms
نویسنده
چکیده
a(p) = 2p~ @ ) cos 0(p). Since we know the truth of the Ramanujan-Petersson conjecture, it follows that the 0(p)'s are real. Inspired by the Sato-Tate conjecture for elliptic curves, Serre [14] conjectured that the 0(p)'s are uniformly distributed in the interval [0, rc] with respect to the 1 measure -sin2OdO. Following Serre, we shall refer to this as the Sato-Tate r~ conjecture, there being no room for confusion. It has been known for a long time that the truth of this conjecture implies much about the oscillatory behaviour of the Fourier coefficients. In particular, the following is implied by the Sato-Tate conjecture. Theorem 1. For any normalized Hecke eigenform,
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تاریخ انتشار 1983