Geodesic
On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms
Yujiao Jiang1 ; Guangshi Lü1
1 Department of Mathematics Shandong University Jinan, Shandong, 250100, China
Acta Arithmetica, Tome 166 (2014) no. 3, pp. 231-252

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $\lambda_f(n)$ be the $n$th normalized Fourier coefficient of a holomorphic or Maass cusp form $f$ for $\mathrm{SL(2,\mathbb{Z})}$. We establish the asymptotic formula for the summatory function $$ \sum_{\substack{n\leq x \\ n\equiv l \,({\rm mod}\, q)}}|\lambda_f(n)|^{2j} $$ as $x\rightarrow \infty,$ where $q$ grows with $x$ in a definite way and $j=2,3,4$.
DOI : 10.4064/aa166-3-2
Keywords: lambda nth normalized fourier coefficient holomorphic maass cusp form mathrm mathbb establish asymptotic formula summatory function sum substack leq equiv mod lambda rightarrow infty where grows definite

Yujiao Jiang 1 ; Guangshi Lü 1

1 Department of Mathematics Shandong University Jinan, Shandong, 250100, China 
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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) no. 3, pp. 231-252. doi: 10.4064/aa166-3-2

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