%0 Journal Article %A Banerjee, Soumyarup %A Dixit, Atul %A Gupta, Shivajee %T Lambert series of logarithm, the derivative of Deninger’s function $R(z),$ and a mean value theorem for $\zeta \left (\frac {1}{2}-it\right )\zeta '\left (\frac {1}{2}+it\right )$ %J Canadian journal of mathematics %D 2024 %P 1695-1730 %V 76 %N 5 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000597/ %R 10.4153/S0008414X23000597 %F 10_4153_S0008414X23000597