@article{Han2026, 
author = {Ying Han and Huixue Lao},
title = {Density results on the coefficients of the triple product    L-functions},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {1382-1411},
keywords = {binary quadratic form, triple product L-function, analytic density, natural density},
url = {https://www.sciopen.com/article/10.3934/math.2026059},
doi = {10.3934/math.2026059},
abstract = {Let        H          k              ∗       denote the set of normalized primitive holomorphic Hecke cusp forms of even integral weight    k for the full modular group. Denote by        λ          f      ×      f      ×      f        (  n  ) the    nth coefficient of the triple product    L-function    L  (  f  ×  f  ×  f  ,  s  ) attached to    f  ∈      H          k              ∗      . Suppose    Q  (      x    _    ) is a primitive integral positive-definite binary quadratic form of fixed discriminant    D  <  0 with the class number    h  (  D  )  =  1. In this paper, we study the distribution of        λ          f      ×      f      ×      f        (  n  ) on the set of all primes and its subset    {  p  :  p  =  Q  (      x    _    )  } and obtain the analytic density and the natural density of the above sets. These results generalize previous ones.}
}