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Let λf (n) be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f(z) ∊ Sk(Г). In this paper, we study the asymptotics for double sum involving Fourier coefficient λi f (n) of cusp forms, where i = 2, 4, 6, 8. [ABSTRACT FROM AUTHOR]

In this paper we consider the mean value of hybrid arithmetic function of the form λ6f (n)σb(n)Øc(n), where λf (n) is the n-th Fourier coefficients of the holomorphic cusp form f, σ(n) is the sum-of-divisors function, Ø(n) is the Euler's totient function. In detail, we prove that for any e > 0, ∑ n⩽x λ6f (n)σb(n)Øc(n) = x(b+c+1)P4(log x) + O(xb+c+631/652+ε); where b; c ∊ ℝ. [ABSTRACT FROM AUTHOR]