The distribution of Fourier coefficients of cusp forms over sparse sequences

Huixue Lao; Ayyadurai Sankaranarayanan

Acta Arithmetica, Tome 166 (2014), p. 101-110 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $λ_{f} (n)$ be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform $f (z) \in S_{k} (Γ)$ . We establish that $\sum_{n \leq x} λ_{f}^{2} (n^{j}) = c_{j} x + O (x^{1 - 2 / ({(j + 1)}^{2} + 1)})$ for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.

Publié le : 2014-01-01

Zbl 1303.11055

EUDML-ID : urn:eudml:doc:279653

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     author = {Huixue Lao and Ayyadurai Sankaranarayanan},
     title = {The distribution of Fourier coefficients of cusp forms over sparse sequences},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {101-110},
     zbl = {1303.11055},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-2-1}
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Huixue Lao; Ayyadurai Sankaranarayanan. The distribution of Fourier coefficients of cusp forms over sparse sequences. Acta Arithmetica, Tome 166 (2014) pp. 101-110. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-2-1/