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Uniform estimates for sums of Fourier coefficients of cusp forms

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Abstract

Let k be an even positive integer and f a holomorphic Hecke eigenform of weight k with respect to the full modular group SL(2, ℕ). Let c n be the nth coefficient of the symmetric square L-function associated to f. We study the uniform bound for the sum C(x) = Σ n≦x c n with respect to the weight k and establish that

$$ C(x) = \sum\limits_{n \leqq x} {c_n } \ll x^{\tfrac{3} {5}} (\log x)^{\tfrac{{22}} {5}} + k^{\tfrac{3} {2}} (\log x)^5 $$

. Other similar results are also established.

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Authors and Affiliations

  1. Department of Mathematics, Shandong University, Jinan, Shandong, 250100, China

    G. S. Lü

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  1. G. S. Lü
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Correspondence to G. S. Lü.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant No. 10701048).

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Lü, G.S. Uniform estimates for sums of Fourier coefficients of cusp forms. Acta Math Hung 124, 83–97 (2009). https://doi.org/10.1007/s10474-009-8153-7

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  • DOI: https://doi.org/10.1007/s10474-009-8153-7

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