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Sums of Fourier coefficients of cusp forms of level D twisted by exponential functions |
Huan LIU() |
School of Mathematics, Shandong University, Jinan 250100, China |
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Abstract Let g be a holomorphic or Maass Hecke newform of level D and nebentypus χD, and let ag(n) be its n-th Fourier coefficient. We consider the sum and prove that S1 has an asymptotic formula when β = 1/2 and αis close to for positive integer and X sufficiently large. And when 0<β<1 and α, β fail to meet the above condition, we obtain upper bounds of S1. We also consider the sum with and prove that S2 has better upper bounds than S1 at some special α and β.
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Keywords
exponential sums
cusp form
Fourier coefficients
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Corresponding Author(s):
Huan LIU
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Issue Date: 20 April 2017
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