@article{Hou2022, 
author = {Fei Hou and Bin Chen},
title = {On triple correlation sums of Fourier coefficients of cusp forms},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {19359-19371},
keywords = {automorphic forms, Fourier coefficients, triple correlation sums},
url = {https://www.sciopen.com/article/10.3934/math.20221063},
doi = {10.3934/math.20221063},
abstract = {Let    p be a prime. In this paper, we study the sum         ∑          m      ≥      1            ∑          n      ≥      1            a    n        λ    g    (  m  )      λ          f        (  m  +  p  n  )    U            (              m        X            )        V            (              n        H            )      for any newforms    g  ∈            B        k    (  1  ) (or              B        λ    ∗    (  1  )) and    f  ∈            B        k    (  p  ) (or              B        λ    ∗    (  p  )), with the aim of determining the explicit dependence on the level, where              a        =  {      a    n    ∈      C    } is an arbitrary complex sequence. As a result, we prove a uniform bound with respect to the level parameter    p, and present that this type of sum is non-trivial for any given    H  ,  X  ≥  2.}
}