We find the sum of series of the form for some special functions . The above series is a generalization of the Riemann zeta function. In particular, we take as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mező’s paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of .
We prove an identity involving generalised Euler-Briggs constants, Euler's constant, and linear forms in logarithms of algebraic numbers. This generalises and gives an alternative proof of an identity of Lehmer (1975). Further, this identity facilitates the investigation of the (conjectural) transcendental nature of generalised Euler-Briggs constants. Earlier investigations of similar type by the present authors involved the interplay between additive and multiplicative characters. This in turn...
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