Timeline for Lower bound of first moment of $L$-function on $\mathrm{GL}(3)$

6 events

when toggle format	what		by	license	comment
Oct 20, 2014 at 13:36	answer	added	H.Flip		timeline score: 4
S Oct 20, 2014 at 5:03	history	edited	Peter Humphries	CC BY-SA 3.0	LaTeX the title and notation
S Oct 20, 2014 at 5:03	history	suggested	Paul	CC BY-SA 3.0	LaTeX the title and notation
Oct 20, 2014 at 4:38	review	Suggested edits
S Oct 20, 2014 at 5:03
Oct 20, 2014 at 2:22	comment	added	Lucia		Yes, this kind of lower bound in $t$-aspect is trivial for any $L$-function. The point is that you can approximate $L(\frac 12+it)$ by some long Dirichlet polynomial $\sum_{n\le T^{r}} a(n)n^{-1/2-it}$, say, with $a(1)=1$, and the $L$-function coming from $GL(r)$, say. If you now integrate with smooth weights $L(1/2+it)$ (without absolute values), then note that only the term $n=1$ contributes. The rest of the terms cancel out and are negligible for smooth weights (rapid decay of Fourier transforms). So the bound $\gg T$ follows.
Oct 20, 2014 at 2:00	history	asked	7-adic	CC BY-SA 3.0