Timeline for Theta Functions and Cousins
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 14, 2009 at 17:15 | comment | added | S. Carnahan♦ | I don't know if it is possible to analytically continue T to the lower half plane. Modular forms tend to yield essential singularities at the boundary of the q-disc - pick a Mobius transformation that takes infinity to a rational number, and feed infinity to a positive weight transformation formula. I'm afraid I also don't know what happens if you try to feed in irrational real numbers. I've heard people mention modular forms definable on the lower half plane, maybe using GL2 instead of SL2, but I know basically nothing there. | |
| Oct 14, 2009 at 16:47 | vote | accept | Chris Schommer-Pries | ||
| Oct 14, 2009 at 16:47 | comment | added | Chris Schommer-Pries | Actually, I decided to leave it as it was. So does T(-z) then make sense on the lower half plane? or is the convergence issue worse then that. What if z is real? Can we make sense of T(z)/T(-z) then? | |
| Oct 14, 2009 at 16:36 | comment | added | Chris Schommer-Pries | I see your point. Yes, I meant for N(v) to be the quadratic form that defines the inner product on the lattice; I forgot the factor of one-half. I think there was another mistake. I'll go fix this a bit. | |
| Oct 14, 2009 at 16:34 | history | edited | S. Carnahan♦ | CC BY-SA 2.5 |
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| Oct 14, 2009 at 16:24 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |