Estimation of Mean Value of Fourier Coefficients in Arithmetic Series
Letf(z)be a holomorphic primitive cusp form of even integral weightk for the full modular group.Denote by λsym4 f(n)the nth normalized coefficient of the Fourier expansion of the 4th symmetric power L-function associated to f.By using the properties of symmetric power L-functions,the average behavior of the Fourier coefficients of the 4th symmetric pow-er L-function over arithmetic progressions is studied in this paper,i.e.∑n≤xn≡l(q) λsym4 f(n2).
holomorphic primitive cusp formsymmetric power L-functionarithmetic pro-gressionsFourier coefficient
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