09/26/2021, 10:47 PM
Here's a graph of \( H_1(s+s_0) \) (so it's not normalized yet) over \( -1 \le \Re(s) \le 4 \) and \( |\Im(s)| \le 2.5 \). You can see a singularity forming and a very regular look to it.
This wouldn't be the extension I'd choose, as it has a wall of singularities along \( \Im(s)=\pi \) and is \( 2 \pi i \) periodic. We'd want to apply the beta-method approach of growing the period to infinity. Not sure how that would work for \( b=1/2 \) at the moment.
Regards, James
This wouldn't be the extension I'd choose, as it has a wall of singularities along \( \Im(s)=\pi \) and is \( 2 \pi i \) periodic. We'd want to apply the beta-method approach of growing the period to infinity. Not sure how that would work for \( b=1/2 \) at the moment.
Regards, James