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

• Autorzy: Yujiao Jiang , Guangshi Lü
• Języki publikacji: EN

Abstrakty

EN

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
$∑_{\substack{n≤x\\ n≡l (mod q)}} |λ_f(n)|^{2j}$
as x → ∞, where q grows with x in a definite way and j = 2,3,4.

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: 166
• Numer: 3
• Strony: 231-252

Daty

wydano

2014

Twórcy

autor

Yujiao Jiang

• Department of Mathematics, Shandong University, Jinan, Shandong, 250100, China

autor

Guangshi Lü

• Department of Mathematics, Shandong University, Jinan, Shandong, 250100, China

Identyfikatory

DOI

10.4064/aa166-3-2