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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.
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참고문헌 (22)
참고문헌 신청
A. Ivi´c / 2001 / On sums of Fourier coefficients of cusp form / IV International Conference “Modern Problems of Number Theory and its Applications”: current problems, part II(R
A. Mukhopadhyay / 2007 / A zero density estimate for the Selberg class / Int. J. Number Theory 3 (2) : 263 ~ 273
A. Sankaranarayanan / 2006 / On a sum involving Fourier coefficients of cusp forms / Lithuanian Math. J 46 (4) : 459 ~ 474
A. Selberg / 1940 / Bemerkungen ¨uber eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist / Arch. Math. Naturvid 43 : 47 ~ 50
F. Shahidi / 1989 / Third symmetric power L-functions for GL(2) / ompos. Math 70 (3) : 245 ~ 273
A. Mukhopadhyay / 2007 / A zero density estimate for the Selberg class / Int. J. Number Theory 3 (2) : 263 ~ 273
A. Sankaranarayanan / 2006 / On a sum involving Fourier coefficients of cusp forms / Lithuanian Math. J 46 (4) : 459 ~ 474
A. Selberg / 1940 / Bemerkungen ¨uber eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist / Arch. Math. Naturvid 43 : 47 ~ 50
F. Shahidi / 1989 / Third symmetric power L-functions for GL(2) / ompos. Math 70 (3) : 245 ~ 273
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