Search results for "Polylogarithm"
showing 3 items of 3 documents
High-energy evolution to three loops
2018
The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to this equation in planar $\mathcal{N}=4$ super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the three-loop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in cross-section calculations in the planar limit. We compare our result in the linear re…
Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six
2017
We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases of the linear spaces generated by the real and imaginary parts of $G(a_1,\ldots,a_w;1)$ and present a table for expressing them as linear combinations of the elements of the bases.
Spatial variability of dry spells duration statistical distributions
2014
Dry spells duration and its extent in space, is a key factor in water resources problems. In order to modelling the empirical distribution of dry spells (DS) frequencies observed in Sicily (i.e. in a typical Mediterranean climate), Agnese et al. (2014) successfully applied the two-parameter polylogarithm-series distribution. Because of the strong seasonality characterising Sicily’s rainfall regime, statistical analysis was separately applied to two data sets, referred to as “dry” and “wet” seasons, respectively. In this work, a similar analysis was carried out for a set of 26 DS time-series recorded in a large area (about 30000 km2), including Piedmont and the Aosta Valley. Area altitude ra…