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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.