Quasi-symmetric functions and mod p multiple harmonic sums

Congruences Involving Alternating Multiple Harmonic Sums

We show that for any prime prime p = 2, p−1 k=1 (−1) k k − 1 2 k ≡ − (p−1)/2 k=1 1 k (mod p 3) by expressing the left-hand side as a combination of alternating multiple harmonic sums.

Mod p structure of alternating and non-alternating multiple harmonic sums

The well-known Wolstenholme’s Theorem says that for every prime p > 3 the (p−1)-st partial sum of the harmonic series is congruent to 0 modulo p2. If one replaces the harmonic series by ∑ k≥1 1/n for k even, then the modulus has to be changed from p2 to just p. One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partia...

Congruences involving alternating multiple harmonic sum

We show that for any prime prime p = 2 p−1 k=1 (−1) k k − 1 2 k ≡ − (p−1)/2 k=1 1 k (mod p 3) by expressing the l.h.s. as a combination of alternating multiple harmonic sums.

Structural relations of harmonic sums and Mellin transforms up to weight w=5

We derive the structural relations between the Mellin transforms of weighted Nielsen integrals emerging in the calculation of massless or massive single–scale quantities in QED and QCD, such as anomalous dimensions and Wilson coefficients, and other hard scattering cross sections depending on a single scale. The set of all multiple harmonic sums up to weight five cover the sums needed in the ca...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points