Addition Theorems, Formal Group Laws and Integrable Systems

V. M. Buchstaber, E. Yu Bunkova

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

We consider elliptic curves, given in the Weierstrass parametrization by the equation y2+μ1xy+μ3y = x3+μ2x2+μ4x+μ6. In Tate coordinates t = -x/y and s = -1/y, the geometric addition laws on this curves correspond to the general elliptic formal group law over the ring Z[μ1,μ2,μ3,μ4,μ6]. This formal group law is well-known in the number theory and cryptography. One can find this law in recent works on the theory of elliptic functions and algebraic topology. In the focus of our interest are questions, important from the point of view of Hirzebruch genera and the theory of integrable systems (see references).

Original languageEnglish
Title of host publicationXXIX Workshop on Geometric Methods in Physics, WGMP 2010
EditorsPiotr Kielanowski, Theodore Voronov, Martin Schlichenmaier, Anatol Odzijewicz, Piotr Kielanowski, Victor Buchstaber
PublisherAmerican Institute of Physics Inc.
Pages33-43
Number of pages11
ISBN (Electronic)9780735408616
DOIs
Publication statusPublished - 2010
Externally publishedYes
Event29th Workshop on Geometric Methods in Physics, WGMP 2010 - Bialowieza, Poland
Duration: 27 Jun 20103 Jul 2010

Publication series

NameAIP Conference Proceedings
Volume1307
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference29th Workshop on Geometric Methods in Physics, WGMP 2010
Country/TerritoryPoland
CityBialowieza
Period27/06/103/07/10

Keywords

  • differential equations for exponentials
  • elliptic functions
  • formal group laws

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