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Sums of Fourier coefficients of cusp forms of level D twisted by exponential functions
Received date: 15 Dec 2015
Accepted date: 04 Mar 2016
Published date: 20 Apr 2017
Copyright
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.
Key words: exponential sums; cusp form; Fourier coefficients
Huan LIU . Sums of Fourier coefficients of cusp forms of level D twisted by exponential functions[J]. Frontiers of Mathematics in China, 2017 , 12(3) : 655 -673 . DOI: 10.1007/s11464-016-0534-y
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