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

Yujiao Jiang, and Guangshi Lü. "On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms." Acta Arithmetica 166.3 (2014): 231-252. <http://eudml.org/doc/278936>.

@article{YujiaoJiang2014,
abstract = {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 $∑_\{\begin\{array\}\{c\}n≤x\\ n≡l (mod q)\end\{array\}\} |λ_f(n)|^\{2j\}$ as x → ∞, where q grows with x in a definite way and j = 2,3,4.},
author = {Yujiao Jiang, Guangshi Lü},
journal = {Acta Arithmetica},
keywords = {Fourier coefficients; arithmetic progression; cusp forms},
language = {eng},
number = {3},
pages = {231-252},
title = {On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms},
url = {http://eudml.org/doc/278936},
volume = {166},
year = {2014},
}

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
VL - 166
IS - 3
SP - 231
EP - 252
AB - 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 $∑_{\begin{array}{c}n≤x\\ n≡l (mod q)\end{array}} |λ_f(n)|^{2j}$ as x → ∞, where q grows with x in a definite way and j = 2,3,4.
LA - eng
KW - Fourier coefficients; arithmetic progression; cusp forms
UR - http://eudml.org/doc/278936
ER -