Johannes Blümlein

TL;DR: In this article, the authors explore the algorithmic and analytic properties of generalized harmonic sums (S-sums) and derive algebraic and structural relations, like differentiation with respect to the external summation index and different multi-argument relations, for the compactification of S-sum expressions.

TL;DR: The Mellin and inverse Mellin transform is work out which connects the sums under consideration with the associated Poincare iterated integrals, also called generalized harmonic polylogarithms, and algebraic and structural relations are derived for the compactification of S-sum expressions.

TL;DR: The analytic continuation of the Mellin transforms to complex values of N for the basic functions gi(x) of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space-and time-like momentum transfer are evaluated in this article.

TL;DR: In this paper, the resummation of O(α s l + 1 ln 2 l x ) terms in the evolution kernels of non-singlet combinations of unpolarized and polarized structure functions is investigated.

TL;DR: In this paper, the static contribution to the gravitational interaction potential of two point masses in the velocity-independent five-loop approximation to the harmonic coordinates effective action in a direct calculation was computed using effective field methods based on Feynman diagrams in momentum-space in d = 3 − 2 e space dimensions.