# The distribution of Fourier coefficients of cusp forms over sparse sequences

Huixue Lao; Ayyadurai Sankaranarayanan

Acta Arithmetica (2014)

- Volume: 163, Issue: 2, page 101-110
- ISSN: 0065-1036

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topHuixue 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 -

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