1Department of Mathematics Shandong Normal University 250014 Jinan, China 2School of Mathematics Tata Institute of Fundamental Research 400005 Mumbai, India
Acta Arithmetica, Tome 163 (2014) no. 2, pp. 101-110
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.
Keywords:
lambda nth normalized fourier coefficient holomorphic hecke eigenform gamma establish sum leq lambda frac which improves previous results even establish better result
Affiliations des auteurs :
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
@article{10_4064_aa163_2_1,
author = {Huixue Lao and Ayyadurai Sankaranarayanan},
title = {The distribution of {Fourier} coefficients of cusp forms over sparse sequences},
journal = {Acta Arithmetica},
pages = {101--110},
year = {2014},
volume = {163},
number = {2},
doi = {10.4064/aa163-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa163-2-1/}
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AU - Ayyadurai Sankaranarayanan
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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
