Geodesic
The distribution of Fourier coefficients of cusp forms over sparse sequences
Huixue Lao 1   ; Ayyadurai Sankaranarayanan 2
1 Department of Mathematics Shandong Normal University 250014 Jinan, China
2 School of Mathematics Tata Institute of Fundamental Research 400005 Mumbai, India
Acta Arithmetica, Tome 163 (2014) no. 2, pp. 101-110 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\lambda_f(n)$ be the $n$th normalized Fourier coefficient of a holomorphic Hecke eigenform $f(z)\in S_{k}(\Gamma)$. We establish that $\sum_{n \leq x}\lambda_f^2(n^j)=c_{j} x+O(x^{1-\frac{2}{(j+1)^2+1}})$ for $j=2,3,4,$ which improves the previous results. For $j=2$, we even establish a better result.
DOI : 10.4064/aa163-2-1
Keywords: lambda nth normalized fourier coefficient holomorphic hecke eigenform gamma establish sum leq lambda frac which improves previous results even establish better result

Huixue Lao  1   ; Ayyadurai Sankaranarayanan  2

1 Department of Mathematics Shandong Normal University 250014 Jinan, China
2 School of Mathematics Tata Institute of Fundamental Research 400005 Mumbai, India 
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     title = {The distribution of {Fourier} coefficients of cusp forms over sparse sequences},
     journal = {Acta Arithmetica},
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Huixue Lao; Ayyadurai Sankaranarayanan. The distribution of Fourier coefficients of cusp forms over sparse sequences. Acta Arithmetica, Tome 163 (2014) no. 2, pp. 101-110. doi: 10.4064/aa163-2-1

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