Timeline for Non-holomorphicity of Hecke regularization of weight-2 level-1 Eisenstein series
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2022 at 23:02 | comment | added | xir | i guess a better way to phrase this is: i'm assuming del bar of the analytic continuation equal to to the analytic continuation of del bar, which is not necessarily accurate. | |
| Aug 31, 2022 at 20:41 | comment | added | xir | i guess the thing i'm implicitly assuming is that applying a differential operator in $\tau$ to an analytic function of $s$ remains analytic in $s$. i'd like to understand better why this fails; is there a simple example of a function $f(x,y)$ analytic in $y$ such that its $x$-derivative acquires a jump discontinuity in $y$ (for some fixed $x$)? | |
| Aug 31, 2022 at 9:23 | comment | added | Lambert A'Campo | Yes but being analytic in $s$ does not imply anything about differentiation in $\tau$ direction. | |
| Aug 30, 2022 at 2:41 | comment | added | xir | isn't the definition of $E_2(\tau,s)$ at $s=0$ via analytic continuation in $s$? and therefore wouldn't the dolbeault operator applied to this function of $s$, analytic at $s=0$, be analytic (and thus continuous) at $s=0$? | |
| Aug 30, 2022 at 0:09 | history | answered | Lambert A'Campo | CC BY-SA 4.0 |