I'm trying to read the article [*"Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups"* by Bukhshtaber,V. M. Russian Mathematical Surveys(1990),45(3):213](http://iopscience.iop.org/article/10.1070/RM1990v045n03ABEH002361/pdf) Russian text is available at [MathNet.ru](http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=4741&option_lang=rus) 


This article gives a general solution of the functional equation
$$f(u+v)=\frac{f(u)^2a(v)-f(v)^2a(u)}{f(u)b(v)-f(v)b(u)}.$$
It leads to [Bukhshtaber] formal group law of the form
$$F(x,y)=\frac{x^2A(y)-y^2A(x)}{xB(y)-yB(x)}.$$


Unfortunately this article contains only a sketch of the proof. Additional typos do not help in decryption.


Are there any references to the full proof of this result? 


Are there any simpler proofs of this result?



Functional equations associated with addition theorems for elliptic functions
There is a more simple proof in the book *V. M. Buchstaber, T. E. Panov, Toric Topology, Mathematical Surveys and Monographs, 204, Amer. Math. Soc., 2015*, [arXiv: 1210.2368v3](http://arxiv.org/abs/1210.2368v3). This result is the theorem E5.4.


