Timeline for Convergence radius of the q-expansion of the modular lambda function
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23, 2011 at 8:45 | history | edited | S. Carnahan♦ | CC BY-SA 3.0 |
Expansion; added 592 characters in body; edited body
|
| Jun 22, 2011 at 18:57 | comment | added | Kevin Buzzard | Alternatively: clearly the series converges for $|q|<1$, because $\lambda$ is a function on the upper half plane. However the coefficients are integers and $\lambda$ is surely known not to be a polynomial (I believe this is a general fact about modular functions), so clearly the function will never converge absolutely for $|q|=1$ and you're home. | |
| Jun 22, 2011 at 12:27 | vote | accept | Ariyan Javanpeykar | ||
| Jun 22, 2011 at 12:25 | comment | added | Ariyan Javanpeykar | I see Junkie made the same comment. | |
| Jun 22, 2011 at 12:05 | comment | added | Ariyan Javanpeykar | So, for all tau in the complex upper half plane, we have that lambda(tau) = sum a_j q(tau)^j? (Here I use that |q(tau)| < R if and only if Im(tau) > log(1/R)/(2pi) .) | |
| Jun 22, 2011 at 11:07 | history | answered | S. Carnahan♦ | CC BY-SA 3.0 |