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Riemann's non-differentiable function and Gauss's quadratic reciprocity lawhave attracted the attention of many researchers. In \cite{RM} Murty andPacelli gave an instructive proof of the quadratic reciprocity via thetheta-transformation formula and Gerver \cite{G1} was the first to give a proofof differentiability/non-differentiability of Riemnan's function. The aim hereis to survey some of the work done in these two questions and concentrates moreonto a recent work of the first author along with Kanemitsu and Li \cite{K1}.In that work \cite{K1} an integrated form of the theta function was utilisedand the advantage of that is that while the theta-function $\Theta(\tau)$ is adweller in the upper-half plane, its integrated form $F(z)$ is a dweller in theextended upper half-plane including the real line, thus making it possible toconsider the behaviour under the increment of the real variable, where theintegration is along the horizontal line.

Quadratic reciprocity and Some "non-differentiable" functions