Geodesic
The average behaviour of a hybrid arithmetic function associated to cusp form coefficients over certain sparse sequence
Filomat, Tome 37 (2023) no. 23, p. 7791

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DOI

Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group Γ = SL(2, Z), and let λ f (n), σ(n) and φ(n) be the nth normalized Fourier coefficient of the cusp form f , the sum-of-divisors function and the Euler totient function, respectively. In this paper, we investigate the asymptotic behaviour of the following summatory function S j,b,c (x) := n=a 2 1 +a 2 2 +a 2 3 +a 2 4 ≤x (a 1 ,a 2 ,a 3 ,a 4)∈Z 4 λ j f (n)σ b (n)φ c (n), where j ≥ 2 is any given integer. In a similar manner, we also establish other similar results related to normalized coefficients of the symmetric power L-functions associated to holomorphic cusp form f .
DOI : 10.2298/FIL2323791H
Classification : 11F11, 11F30, 11F66
Keywords: Hecke eigenvalues, Holomorphic cusp forms, Automorphic L-functions 
Guodong Hua. The average behaviour of a hybrid arithmetic function associated to cusp form coefficients over certain sparse sequence. Filomat, Tome 37 (2023) no. 23, p. 7791 . doi: 10.2298/FIL2323791H
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     title = {The average behaviour of a hybrid arithmetic function associated to cusp form coefficients over certain sparse sequence},
     journal = {Filomat},
     pages = {7791 },
     year = {2023},
     volume = {37},
     number = {23},
     doi = {10.2298/FIL2323791H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2323791H/}
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