The distribution of Fourier coefficients of cusp forms over sparse sequences Huixue Lao; Ayyadurai Sankaranarayanan — 2014 Acta Arithmetica Let λ f ( n ) be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform f ( z ) ∈ S k ( Γ ) . We establish that ∑ n ≤ x λ f 2 ( n j ) = c j x + O ( x 1 - 2 / ( ( j + 1 ) 2 + 1 ) ) for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.