Fundamental Domains of Gamma and Zeta Functions

Details Fundamental Domains of Gamma and Zeta Functions Fundamental Domains of Gamma and Zeta Functions

2009-11-26

arxiv.org/abs/0911.5138v3

Mathematics

Complex Variables

14 pages, 10 figures

Scientific paper

Branched covering Riemann surfaces $(\mathbb{C},f)$ are studied, where $f$ is the Euler Gamma function and the Riemann Zeta function. For both of them fundamental domains are found and the group of covering transformations is revealed. In order to find fundamental domains, pre-images of the real axis are taken and a thorough study of their geometry is performed. The technique of simultaneous continuation, introduced by the authors in previous papers, is used for this purpose. Color visualization of the conformal mapping of the complex plane by these functions is used for a better understanding of the theory. For the Riemann Zeta function the outstanding question of the multiplicity of its zeros, as well as of the zeros of its derivative is answered.

Affiliated with

Also associated with

No associations

Rating

Fundamental Domains of Gamma and Zeta Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fundamental Domains of Gamma and Zeta Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fundamental Domains of Gamma and Zeta Functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-117013