Timeline for Is there any literature on multivariable theta functions?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23, 2010 at 4:51 | vote | accept | Simon Rose | ||
| Jun 23, 2010 at 2:29 | comment | added | Victor Protsak | Theta functions depend to two variables, $\tau$ in the Siegel upper half-plane $S_g$ and $z$ in $\mathbb{C}^g.$ Your theta function of the lattice $\vartheta_\Lambda$ (corresponding to $g=1$ is known as a theta-$\textit{constant},$ precisely because the "main" variable $z$ has been set to $0.$ Mumford's book explains it well. Let me just add that the role of the lattice is complementary: it accounts for the Howe duality between an auxiliary orthogonal group $O(\Lambda)$ of isometries of $\Lambda$ and the symplectic group $Sp_{2g}.$ | |
| Jun 23, 2010 at 0:18 | comment | added | Wadim Zudilin | There is a very nice old (around 1900) book of Krazer on theta functions in several variables (it's in German). Otherwise Mumford's Tata lectures on theta are still very comprehensive. There was a 2-volume proceedings edition of a conference on Theta functions (published by AMS in 1989); it contains some good surveys on the subject. | |
| Jun 22, 2010 at 23:13 | answer | added | SandeepJ | timeline score: 7 | |
| Jun 22, 2010 at 20:49 | answer | added | S. Carnahan♦ | timeline score: 2 | |
| Jun 22, 2010 at 20:31 | comment | added | Helge | The ones for Z^g have applications to completely integrable systems. See mat.univie.ac.at/~gerald/ftp/book-jac/jacop.pdf . Or the book by Gesztesy, Holden, Michor, and Teschl (not available online, afaik). | |
| Jun 22, 2010 at 19:01 | history | asked | Simon Rose | CC BY-SA 2.5 |