Theta Functions on Riemann Surfaces

1973 ◽  
Author(s):  
John D. Fay
Keyword(s):  
Riemann Surfaces ◽  
Theta Functions

Elliptic Functions, Theta Functions, and Riemann Surfaces

1974 ◽  
Vol 28 (127) ◽  
pp. 875
Author(s):  
Y. L. L. ◽  
Harry E. Rauch ◽  
Aaron Lebowitz
Keyword(s):  
Riemann Surfaces ◽  
Theta Functions ◽  
Elliptic Functions

LEVEL-ONE SU(N) WZNW MODELS ON HIGHER-GENUS RIEMANN SURFACES

1993 ◽  
Vol 08 (17) ◽  
pp. 2955-2972 ◽  
Author(s):  
M. ALIMOHAMMADI ◽  
H. ARFAEI
Keyword(s):  
Partition Function ◽  
Simple Form ◽  
Riemann Surfaces ◽  
Theta Functions ◽  
Modular Invariance ◽  
Fusion Rules ◽  
Group Manifold ◽  
Special Cases ◽  
Wznw Model ◽  
Higher Genus

Using factorization properties and fusion rules, we find the higher-genus partition function and two-point correlators for the SU (N)1 WZNW model. The result has simple form in terms of higher-genus theta functions on the group manifold. The previously known results of SU (2)1 and SU (3)1 are also obtained as special cases. This method, combined with other considerations such as modular invariance, can be extended to the nonsimply laced groups and higher-level WZNW models.

scholarly journals On the Hyperelliptic Riemann Surfaces of Infinite Genus with Absolutely Convergent Riemann’s Theta Functions

1968 ◽  
Vol 33 ◽  
pp. 57-73 ◽  
Author(s):  
Kenichi Tahara
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Theta Functions ◽  
Hyperelliptic Riemann Surfaces ◽  
Hyperelliptic Riemann Surface ◽  
Closed Riemann Surface

The Riemann’s theta functions associated with a closed Riemann surface are absolutely convergent. In the present paper, we shall show an example of an hyperelliptic Riemann surface of infinite genus such that the Riemann’s theta functions associated with are absolutely convergent.

30 years of finite-gap integration theory

2007 ◽  
Vol 366 (1867) ◽  
pp. 837-875 ◽  
Author(s):  
Vladimir B Matveev
Keyword(s):  
Algebraic Geometry ◽  
Riemann Surfaces ◽  
Theta Functions ◽  
Theoretical Physics ◽  
Integration Theory ◽  
Difference Operators ◽  
Strong Impact ◽  
Riemann Theta Functions ◽  
Compact Riemann Surfaces ◽  
Modern Mathematics

The method of finite-gap integration was created to solve the periodic KdV initial problem. Its development during last 30 years, combining the spectral theory of differential and difference operators with periodic coefficients, the algebraic geometry of compact Riemann surfaces and their Jacobians, the Riemann theta functions and inverse problems, had a strong impact on the evolution of modern mathematics and theoretical physics. This article explains some of the principal historical points in the creation of this method during the period 1973–1976, and briefly comments on its evolution during the last 30 years.

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