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Abstract Let λ i ( n ) , i = 1 , 2 , 3 , denote the normalized Fourier coefficients of a holomorphic eigenform or Maass cusp form. In… Click to show full abstract
Abstract Let λ i ( n ) , i = 1 , 2 , 3 , denote the normalized Fourier coefficients of a holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum: S : = 1 H ∑ H ≤ h ≤ 2 H V ( h H ) × ∑ N ≤ n ≤ 2 N λ 1 ( n ) λ 2 ( n + h ) λ 3 ( n + 2 h ) W ( n N ) , where V and W are smooth bump functions, supported on [ 1 , 2 ] . We shall prove a nontrivial upper bound, under the assumption that H ≥ N 1 / 2 + ϵ .
Keywords:
convolution sum;
double shifted;
shifted convolution;
sum hecke;
hecke eigenforms
Journal Title: Journal of Number Theory
Year Published: 2018
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Journal Title: Journal of Number Theory
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!