Distribution of Hecke eigenvalues of newforms in short intervals

Abstract : We explore nonvanishing of Hecke eigenvalues in short arithmetic progressions and their signs in short intervals by further developing B-free number method and studying moments in short intervals. We improve some results of Alkan & Zaharescu [3] and Lau & Wu [20] on the distribution of Hecke eigenvalues.
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Jie Wu, Wenguang Zhai. Distribution of Hecke eigenvalues of newforms in short intervals. Quarterly Journal of Mathematics, Oxford University Press (OUP), 2013, 64 (2), pp.619-644. ⟨10.1093/qmath/has007⟩. ⟨hal-01278937⟩

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