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Ω-RESULT ON COEFFICIENTS OF AUTOMORPHIC L-FUNCTIONS OVER SPARSE SEQUENCES

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Let λ∫(n) denote the n-th normalized Fourier coefficient of a primitive holomorphic form ∫ for the full modular group Γ = SL2(Z). In this paper, we are concerned with Ω-result on the summatory function Σn≤xλ2∫(n2), and establish the following result Σn≤xλ2∫(n2) = c1x + Ω(x4/9), where c1 is a suitable constant.

Abstract

Let λ∫(n) denote the n-th normalized Fourier coefficient of a primitive holomorphic form ∫ for the full modular group Γ = SL2(Z). In this paper, we are concerned with Ω-result on the summatory function Σn≤xλ2∫(n2), and establish the following result Σn≤xλ2∫(n2) = c1x + Ω(x4/9), where c1 is a suitable constant.

참고문헌 (22)

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