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

2018/09/25 by Ashton, A. C. L., Fokas, A. S.
#11L07 #11M35 #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.09440

Abstract

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 if the important results of [11]. 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 ζ₁(s,α), s∈ C, α∈ R, which is also presented here.

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