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math.NT2021★ 3 cited
A note on some infinite sums of Hurwitz zeta functions
R B Paris
We consider some closed-form evaluations of certain infinite sums involving the Hurwitz zeta function of the form \[\sum_{k=1}^\infty (\pm 1)^k k^m ζ(s,k),\] where is…
math.NT2020
On some Féjer-type trigonometric sums
R. B. Paris
We examine the four Féjer-type trigonometric sums of the form \[S_n(x)=\sum_{k=1}^n \frac{f(g(kx))}{k}\qquad (0<x<π)\] where , are chosen to be either or $\co…