Geodesic
On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms
Yujiao Jiang 1   ; Guangshi Lü 1
1 Department of Mathematics Shandong University Jinan, Shandong, 250100, China
Acta Arithmetica, Tome 166 (2014) no. 3, pp. 231-252 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_aa166_3_2,
     author = {Yujiao Jiang and Guangshi L\"u},
     title = {On the higher mean over arithmetic progressions
 of {Fourier} coefficients of cusp forms},
     journal = {Acta Arithmetica},
     pages = {231--252},
     year = {2014},
     volume = {166},
     number = {3},
     doi = {10.4064/aa166-3-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa166-3-2/}
}
TY  - JOUR
AU  - Yujiao Jiang
AU  - Guangshi Lü
TI  - On the higher mean over arithmetic progressions
 of Fourier coefficients of cusp forms
JO  - Acta Arithmetica
PY  - 2014
SP  - 231
EP  - 252
VL  - 166
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa166-3-2/
DO  - 10.4064/aa166-3-2
LA  - en
ID  - 10_4064_aa166_3_2
ER  - 
%0 Journal Article
%A Yujiao Jiang
%A Guangshi Lü
%T On the higher mean over arithmetic progressions
 of Fourier coefficients of cusp forms
%J Acta Arithmetica
%D 2014
%P 231-252
%V 166
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/aa166-3-2/
%R 10.4064/aa166-3-2
%G en
%F 10_4064_aa166_3_2
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

Cité par Sources :