Meromorphic functions on compact Riemann surfaces and value sharing

2005 ◽  
Vol 50 (15) ◽  
pp. 1163-1164 ◽  
Author(s):  
E. Ballico
Keyword(s):  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Value Sharing ◽  
Compact Riemann Surfaces

scholarly journals THE RESIDUE THEOREM AND AN ANALOG OF P. APPELL’S FORMULA FOR FINITE RIEMANN SURFACES

2016 ◽  
pp. 40-45
Author(s):  
Viktor Chueshev ◽  
Viktor Chueshev ◽  
Aleksandr Chueshev ◽  
Aleksandr Chueshev
Keyword(s):  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Function Theory ◽  
Mathematical Physics ◽  
General Function ◽  
Multiplicative Functions ◽  
Residue Theorem ◽  
Equations Of Mathematical Physics ◽  
Compact Riemann Surfaces ◽  
Integral Order

A theory of multiplicative functions and Prym differentials for the case of special characters on compact Riemann surfaces has found applications in geometrical function theory of complex variable, analytical number theory and in equations of mathematical physics. Theory of functions on compact Riemann surfaces differs from the theory of functions on finite Riemann surfaces even for the class of single meromorphic functions and Abelian differentials. In this article we continue the construction of the general function theory on finite Riemann surfaces for multiplicative meromorphic functions and differentials. We have proved analogues of the theorem on the full sum of residues for Prym differentials of every integral order and P. Appell's formula on expansion of the multiplicative function with poles of arbitrary multiplicity in the sum of elementary Prym integrals.

Rings of Meromorphic Functions on Non-Compact Riemann Surfaces

1969 ◽  
Vol 21 ◽  
pp. 284-300 ◽  
Author(s):  
James Kelleher
Keyword(s):  
Riemann Surface ◽  
Algebraic Structure ◽  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Doctoral Dissertation ◽  
University Of Illinois ◽  
Compact Riemann Surfaces ◽  
The University ◽  
Complex Valued

In this paper we shall be concerned with the algebraic structure of certain rings of functions meromorphic on a non-compact (connected) Riemann surface Ω. In this setting, A = A(Ω) and K= K(Ω) denote (respectively) the ring of all complex-valued functions analytic on Ω and its field of quotients, the field of functions meromorphic on Ω. The rings considered here are those subrings of K containing A,which we term A-rings of K. Most of the results given here were previously announced without proof (15) and are contained in the author's doctoral dissertation (16), completed at the University of Illinois under the direction of Professor M. Heins, whose encouragement and advice are gratefully acknowledged.

On Rings with a Certain Type of Factorization and Compact Riemann Surfaces

1990 ◽  
Vol 42 (6) ◽  
pp. 1041-1052
Author(s):  
Pascual Cutillas Ripoll
Keyword(s):  
Riemann Surface ◽  
Finite Subset ◽  
Riemann Surfaces ◽  
Compact Riemann Surface ◽  
Meromorphic Functions ◽  
Irreducible Elements ◽  
Finite Sums ◽  
Compact Riemann Surfaces

AbstractLet be a compact Riemann surface, be the complement of a nonvoid finite subset of and A() be the ring of finite sums of meromorphic functions in with finite divisor. In this paper it is proved that every nonzero f ∈ A() can be decomposed as a product αβ, where α is either a unit or a product of powers of irreducible elements of A(), uniquely determined by f up to multiplication by units, and β is a product of functions of the type eφ – 1, with φ holomorphic and nonconstant in . Furthermore, a similar result is obtained for a certain class of subrings of A().

scholarly journals Vector Bundle of Prym Differentials over Teichm¨uller Spaces of Surfaces with Punctures

2019 ◽  
pp. 263-275
Author(s):  
Alexander V. Chueshev ◽  
Victor V. Chueshev
Keyword(s):  
Vector Bundle ◽  
Finite Type ◽  
Riemann Surfaces ◽  
Vector Bundles ◽  
Meromorphic Functions ◽  
Multiplicative Functions ◽  
Quotient Spaces ◽  
Abelian Differentials ◽  
Compact Riemann Surfaces

In this paper we study multiplicative meromorphic functions and differentials on Riemann surfaces of finite type. We prove an analog of P. Appell’s formula on decomposition of multiplicative functions with poles of arbitrary multiplicity into a sum of elementary Prym integrals. We construct explicit bases for some important quotient spaces and prove a theorem on a fiber isomorphism of vector bundles and n!-sheeted mappings over Teichm¨uller spaces. This theorem gives an important relation between spaces of Prym differentials (Abelian differentials) on a compact Riemann surfaces and on a Riemann surfaces of finite type

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