Power Residues of Fourier Coefficients of Modular Forms
نویسنده
چکیده
In fact, we suspect that much more is true: we conjecture that this relative density does not change after restriction to any set of primes defined by a Cebatorevstyle Frobenius condition; that is, we expect that the sets (0.1) yield sets of primes of positive density which are quite different from those sets determined by Galois theoretic conditions. See Conjecture 1.2 for a precise statement. For CM-forms f and certain values of m the set (0.1) is in fact defined by Galois theoretic conditions. We use this to prove the following result; see Theorems 3.3, 4.2, and 4.3 for precise statements. (In particular, Theorem 3.3 includes the cases d = 1, 3 when m = 2.)
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