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Several relations are obtained among the Riemann zeta and Hurwitz zetafunctions, as well as their products. A particular case of these relations giverise to a simple re-derivation if the important results of [11]. Also, arelation derived here provides the starting point of a novel approach which ina series of companion papers yields a formal proof of the Lindel\"{o}fhypothesis. Some of the above relations motivate the need for analysing thelarge $\alpha$ behaviour of the modified Hurwitz zeta function$\zeta_1(s,\alpha)$, $s\in \mathbf{C}$, $\alpha\in \mathbf{R}$, which is alsopresented here.

Relations among the Riemann zeta and Hurwitz zeta functions as well as their products