Threshold resummation of the structure function FL

The behaviour of the quark coefficient function for the longitudinal structure function F-L in deep-inelastic scattering is investigated for large values of the Bjorken variable x. We combine a highly plausible conjecture on the large-x limit of the physical evolution kernel for this quantity with our explicit three-loop results to derive the coefficients of the three leading large-x logarithms, alpha(n)(s) ln (2n-1-k(1-x)), k = 1, 2, 3, to all orders in the strong coupling constant alpha(s). Corresponding results are derived for the non-C-F part of the gluon coefficient function suppressed by a factor 1 - x, and for the analogous sub-leading (1 - x) ln(k)(1 - x) contributions in the quark case. Our results appear to indicate an obstacle for an exponentiation with a higher logarithmic accuracy.