In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelöf hypothesis. Some of the above relations motivate the need for analysing the large α behaviour of the modified Hurwitz zeta function ζ 1 ( s , α ) , s ∈ C , α ∈ ( 0 , ∞ ) , which is also presented here.
Complex Zeros of Two Incomplete Riemann Zeta Functions