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The validity of a previously proposed momentum space ansatz for thresholdresummation of the non-singlet longitudinal structure function F_L is checkedagainst existing finite order three-loop results. It is found that the ansatz,which is an assumption for the large-x behavior of the physical evolutionkernel, does not work beyond the leading logarithmic contributions to thekernel even at {\cal O}(1/(1-x)) order (except at large-\beta_0), which isconsistent with a recent observation of Moch and Vogt. Corrections down by onepower of 1-x are also studied. At {\cal O}((1-x)^0) order, the correspondingansatz fails already at the leading logarithmic level, where the situationappears similar to that encountered in the case of the F_i (i=1,2,3) structurefunctions. At the next-to-leading logarithmic level, the same term (withopposite sign) responsible for the failure of the ansatz at {\cal O}(1/(1-x))order is found to occur.

On threshold resummation of the longitudinal structure function