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 Russian text is available at MathNet.ru

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?

  • $\begingroup$ There 23 references to this paper on mathnet. For sure something useful in them. $\endgroup$
    – Sergei
    Apr 19, 2016 at 13:46
  • $\begingroup$ @Sergei No, they contain almost the same information as in my question. $\endgroup$ Apr 19, 2016 at 13:56

1 Answer 1


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. This result is the theorem E5.4.


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