The distribution of Fourier coefficients of cusp forms over sparse sequences

• Autorzy: Huixue Lao , Ayyadurai Sankaranarayanan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11F30: Fourier coefficients of automorphic forms
• 11F66: Langlands L -functions; one variable Dirichlet series and functional equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 2
• Strony: 101-110

Daty

wydano

2014

Twórcy

autor

Huixue Lao

• Department of Mathematics, Shandong Normal University, 250014 Jinan, China

autor

Ayyadurai Sankaranarayanan

• School of Mathematics, Tata Institute of Fundamental Research, 400005 Mumbai, India

Identyfikatory

DOI

10.4064/aa163-2-1