scholarly journals Period Matrices of Real Riemann Surfaces and Fundamental Domains

2013 ◽  
Author(s):  
Pietro Giavedoni
Keyword(s):  
Riemann Surfaces ◽  
Fundamental Domains ◽  
Real Riemann Surfaces

scholarly journals Fundamental Domains of Gamma and Zeta Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Cabiria Andreian Cazacu ◽  
Dorin Ghisa
Keyword(s):  
Conformal Mapping ◽  
Gamma Function ◽  
Riemann Zeta Function ◽  
Riemann Surfaces ◽  
Zeta Functions ◽  
Branched Covering ◽  
Fundamental Domains ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Color Visualization

Branched covering Riemann surfaces(ℂ,f)are studied, wherefis 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.

scholarly journals A Class of Pseudo-Real Riemann Surfaces with Diagonal Automorphism Group

2020 ◽  
Vol 27 (02) ◽  
pp. 247-262
Author(s):  
Eslam Badr
Keyword(s):  
Riemann Surface ◽  
Automorphism Group ◽  
Riemann Surfaces ◽  
Real Plane ◽  
Plane Model ◽  
Field Of Moduli ◽  
Field Of Definition ◽  
Smooth Plane ◽  
Real Riemann Surfaces ◽  
Even Order

A Riemann surface [Formula: see text] having field of moduli ℝ, but not a field of definition, is called pseudo-real. This means that [Formula: see text] has anticonformal automorphisms, but none of them is an involution. A Riemann surface is said to be plane if it can be described by a smooth plane model of some degree d ≥ 4 in [Formula: see text]. We characterize pseudo-real-plane Riemann surfaces [Formula: see text], whose conformal automorphism group Aut+([Formula: see text]) is PGL3(ℂ)-conjugate to a finite non-trivial group that leaves invariant infinitely many points of [Formula: see text]. In particular, we show that such pseudo-real-plane Riemann surfaces exist only if Aut+([Formula: see text]) is cyclic of even order n dividing the degree d. Explicit families of pseudo-real-plane Riemann surfaces are given for any degree d = 2pm with m > 1 odd, p prime and n = d/p.

scholarly journals Automorphism Groups of Symmetric and Pseudo-real Riemann Surfaces

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Ewa Tyszkowska
Keyword(s):  
Riemann Surfaces ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Automorphism Groups ◽  
Real Riemann Surfaces ◽  
Compact Riemann Surfaces

AbstractThe category of smooth, irreducible, projective, complex algebraic curves is equivalent to the category of compact Riemann surfaces. We study automorphism groups of Riemann surfaces which are equivalent to complex algebraic curves with real moduli. A complex algebraic curve C has real moduli when the corresponding surface $$X_C$$ X C admits an anti-conformal automorphism. If no such an automorphism is an involution (symmetry), then the surface $$X_C$$ X C is called pseudo-real and the curve C is isomorphic to its conjugate, but is not definable over reals. Otherwise, the surface $$X_C$$ X C is called symmetric and the curve C is real.

scholarly journals Pseudo-real Riemann surfaces and chiral regular maps

2010 ◽  
Vol 362 (07) ◽  
pp. 3365-3376 ◽  
Author(s):  
Emilio Bujalance ◽  
Marston D. E. Conder ◽  
Antonio F. Costa
Keyword(s):  
Riemann Surfaces ◽  
Regular Maps ◽  
Real Riemann Surfaces

scholarly journals Minimal genus problem for pseudo-real Riemann surfaces

2010 ◽  
Vol 95 (5) ◽  
pp. 481-492 ◽  
Author(s):  
Czesław Bagiński ◽  
Grzegorz Gromadzki
Keyword(s):  
Riemann Surfaces ◽  
Minimal Genus ◽  
Real Riemann Surfaces
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