On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms

Yujiao Jiang; Guangshi Lü

Acta Arithmetica, Tome 166 (2014), p. 231-252 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $λ_{f} (n)$ be the nth normalized Fourier coefficient of a holomorphic or Maass cusp form f for SL(2,ℤ). We establish the asymptotic formula for the summatory function $\sum_{\begin{matrix} n \leq x \\ n \equiv l (m o d q) \end{matrix}} {| λ_{f} (n) |}^{2 j}$ as x → ∞, where q grows with x in a definite way and j = 2,3,4.

Publié le : 2014-01-01

Zbl 1323.11023

EUDML-ID : urn:eudml:doc:278936

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     author = {Yujiao Jiang and Guangshi L\"u},
     title = {On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {231-252},
     zbl = {1323.11023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-2}
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Yujiao Jiang; Guangshi Lü. On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms. Acta Arithmetica, Tome 166 (2014) pp. 231-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-2/