NAME:      Zhi-Guo Liu                    
 
ADDRESS:   Xinxiang Education   College 
           Xinxiang, Henan   453000    
           P. R.  China               
 
EMAIL ADDRESS:   xxlzg@public. xxptt.ha. cn  
 
TITLE OF TALK: Some Eisenstein Series Identities 
               Associated With The Borweins Functions            
 
ABSTRACT OF TALK:
     In this note, we will derive some Eisentein 
series identities associated with the  Borweins functions 
based on a well-known identity involving theta-functions and the method of  
logarithmic differentiation. We will derive some theta-function identities
involving the Borwein functions by employing the theory of elliptic 
functions. From these theta-function identities we give different
approachs to the Eisenstein series identities involving the Borweins 
function.    By using some Eisentein series identities of this note,
we provide completely new proofs of the Borweins' cubic 
theta function identity and the well-known Jacobi identity 
in the theory of modular forms.
 
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