Timeline for Petersson-product of the cusp part of the theta series
Current License: CC BY-SA 3.0
4 events
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| Nov 14, 2014 at 16:05 | comment | added | Jeremy Rouse | Abdullah - Giving explicit lower bounds is difficult when $f$ is a "CM form". This is connected with the problem of $L$-functions having Siegel zeroes. Even in other cases, $\langle f, f \rangle$ can be small. For example, if $f = \Delta$ is usual weight $12$ modular form, $\langle \Delta, \Delta \rangle \approx 9.887 \cdot 10^{-7}$. | |
| Nov 14, 2014 at 14:43 | comment | added | Abdullah.Y | Another Question: Do you Know a lower bound b for $<f,f>$, if $f\in S_k(\Gamma_0(N),\chi)$ is a primitive form? I think $<f,f> \ge 1$ for all primitive forms. Is that right? | |
| Nov 14, 2014 at 10:22 | comment | added | Abdullah.Y | Thank you Jeremy. I have read the paper by Fomenko. He had proven there the case 2k = 4 and that is some time ago, I thought that the general case is probably already proved. The reference of Schulze -Pillot (He is my Mentor for my Masterthesis) was the reason why I looked at Fermenko. You are a great help - now i know it is a difficult problem :) | |
| Nov 13, 2014 at 18:03 | history | answered | Jeremy Rouse | CC BY-SA 3.0 |