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Fundamental Domains of Gamma and Zeta Functions

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  • Cabiria Andreian Cazacu
  • Dorin Ghisa

Abstract

Branched covering Riemann surfaces are studied, where is the Euler Gamma function and the Riemann Zeta function. For both of them fundamental domains are found and the group of cover transformations is revealed. In order to find fundamental domains, preimages 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. A version of this paper containing colored images can be found in arXiv at Andrian Cazacu and Ghisa.

Suggested Citation

  • Cabiria Andreian Cazacu & Dorin Ghisa, 2011. "Fundamental Domains of Gamma and Zeta Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-21, May.
    • Handle: RePEc:hin:jijmms:985323
    DOI: 10.1155/2011/985323
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