Abstract:Let f be a non-CM Hecke eigencusp form of level 1 and fixed weight, and let {λ f (n)}n be its sequence of normalized Fourier coefficients. We show that if K/Q is any number field, and N K denotes the collection of integers representable as norms of integral ideals of K, then a positive proportion of the positive integers n ∈ N K yield a sign change for the sequenceFor example, for K = Q(i) and N K = {m 2 + n 2 : m, n ∈ Z} the set of sums of two squares, we obtain ≫ f X/ √ log X such sign changes, which is best… Show more
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