  The purpose of the paper is to study the uniqueness problem of a $L$ function
in the Selberg class sharing one or two sets with an arbitrary meromorphic
function having finite poles. We manipulate the notion of weighted sharing of
sets to improve one result of Yuan-Li-Yi [Value distribution of $L$-functions
and uniqueness questions of F. Gross, Lithuanian Math. J.,
$\mathbf{58(2)}$(2018), 249-262]. More importantly, we have pointed out a
number of gaps in all the results of Sahoo-Halder [Results on $L$ functions and
certain uniqueness question of Gross, Lithuanian Math. J.,
$\mathbf{60(1)}$(2020), 80-91] which actually makes the validity of the same
paper under question. As an attempt to rectify the results of Sahoo-Halder we
have presented the accurate forms and proof of the results in a compact and
convenient manner.
