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http://dx.doi.org/10.4134/JKMS.2015.52.5.945

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

LAO, HUIXUE (Department of Mathematics Shandong Normal University)
WEI, HONGBIN (Department of Mathematics Shandong Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 945-954 More about this Journal
Abstract
Let ${\lambda}_f(n)$ denote the n-th normalized Fourier coefficient of a primitive holomorphic form f for the full modular group ${\Gamma}=SL_2({\mathbb{Z}})$. In this paper, we are concerned with ${\Omega}$-result on the summatory function ${\sum}_{n{\leqslant}x}{\lambda}^2_f(n^2)$, and establish the following result ${\sum}_{\leqslant}{\lambda}^2_f(n^2)=c_1x+{\Omega}(x^{\frac{4}{9}})$, where $c_1$ is a suitable constant.
Keywords
automorphic L-functions; holomorphic cusp forms; Omega theorem;
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