The distribution of Fourier coefficients of cusp forms over sparse sequences

Huixue Lao, and Ayyadurai Sankaranarayanan. "The distribution of Fourier coefficients of cusp forms over sparse sequences." Acta Arithmetica 163.2 (2014): 101-110. <http://eudml.org/doc/279653>.

@article{HuixueLao2014,
abstract = {Let $λ_f(n)$ be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform $f(z) ∈ S_\{k\}(Γ)$. We establish that $∑_\{n ≤ x\}λ_f^2(n^j) = c_\{j\} x + O(x^\{1-2/((j+1)^2+1)\})$ for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.},
author = {Huixue Lao, Ayyadurai Sankaranarayanan},
journal = {Acta Arithmetica},
keywords = {Fourier coefficients of cusp forms; symmetric power -function; Rankin-Selberg -function},
language = {eng},
number = {2},
pages = {101-110},
title = {The distribution of Fourier coefficients of cusp forms over sparse sequences},
url = {http://eudml.org/doc/279653},
volume = {163},
year = {2014},
}

TY - JOUR
AU - Huixue Lao
AU - Ayyadurai Sankaranarayanan
TI - The distribution of Fourier coefficients of cusp forms over sparse sequences
JO - Acta Arithmetica
PY - 2014
VL - 163
IS - 2
SP - 101
EP - 110
AB - Let $λ_f(n)$ be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform $f(z) ∈ S_{k}(Γ)$. We establish that $∑_{n ≤ x}λ_f^2(n^j) = c_{j} x + O(x^{1-2/((j+1)^2+1)})$ for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.
LA - eng
KW - Fourier coefficients of cusp forms; symmetric power -function; Rankin-Selberg -function
UR - http://eudml.org/doc/279653
ER -