Timeline for Is there an nontrivial function whose 'period paralellograms' are Gosper Islands?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2013 at 11:47 | comment | added | john mangual | I wonder how the choice of fundamental domain alters the discussion of elliptic curves | |
| May 23, 2010 at 20:09 | comment | added | Qiaochu Yuan | The point of Harald's comment is that there is no 'canonical' fundamental domain, at least until you provide extra data. | |
| May 23, 2010 at 14:21 | answer | added | S. Carnahan♦ | timeline score: 2 | |
| May 23, 2010 at 13:55 | comment | added | graveolensa | Harald -- the crux of my question is whether any functions exist whose 'canonical' fundamental domain is a Gosper island -- if you were to look at domain colored pictures of these hypothetical functions, one would say "aha, Gosper islands" instead of "aha, period parallelograms". | |
| May 23, 2010 at 12:02 | history | edited | Wadim Zudilin |
edited tags
|
|
| May 23, 2010 at 11:56 | comment | added | Harald Hanche-Olsen | I don't think the question makes sense. An elliptic function has a period lattice $\Omega$, which is a subgroup of $\mathbb{C}$. There is nothing unique about “the” period parallellogram, though; it is just a convenient labeling of the equivalence classes $\mathbb{C}/\Omega$ by taking one element from each equivalence class. There is no reason, apart from convenience, why it has to be a parallellogram. Gosper islands should do just fine, though to go and pick a fractal one seems slightly perverse. | |
| May 23, 2010 at 11:54 | comment | added | Wadim Zudilin | Dear Deoxy, your source for learning elliptic functions is definitely not the best one. But already there it's explained that fundamental domains of elliptic functions are parallelograms (quotients of $\mathbb C$ by lattices), no snowflakes. More exotic fundamental domains can be constructed for automorphic rather than elliptic functions. I wonder whether one can get fractals but tiling pictures of more regular geometric structure can be seen for example in M.Yoshida's "Hypergeometric functions, my love" (1997). | |
| May 23, 2010 at 11:28 | history | asked | graveolensa | CC BY-SA 2.5 |