Timeline for Fantastic properties of Z/2Z
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2018 at 13:47 | comment | added | Sylvain JULIEN | I strongly doubt it. As far as I know, I'm probably the only person to consider RH might be true investigating the symmetries of $ \zeta $ or equivalently of the multiset of non trivial zeroes thereof. I'd be glad to be proven wrong though. | |
| Jan 8, 2018 at 12:33 | comment | added | bonif | Has this been published somewhere? Coming from the theoretical physics camp I can see off the top of my head there are some possible immediate physical analogies with this. | |
| Jan 8, 2018 at 12:06 | comment | added | Sylvain JULIEN | ...symmetry $ s\mapsto 1-\bar{s} $ and hence generates a global symmetry group isomorphic to $ \Z/2\Z\times\Z/2\Z $. As I said, the absence of zero off the line forces the maps $s\mapsto s $ and $ s\mapsto 1-\bar{s} $ to coincide, reducing the global isometry group to a single copy of $ \Z/2\Z $ . | |
| Jan 8, 2018 at 12:03 | comment | added | Sylvain JULIEN | From the functional equation of $ \zeta $, a hypothetical non trivial zero off the critical line gives rise to a second one which is its image under the map $s\mapsto 1-\bar{s} $. This map coincides with identity for zeroes on this line. As the Dirichlet coefficients of $ \zeta $ are real, the map $ s\mapsto\bar{s} $ maps a non trivial zero of zeta to a non trivial zero of $ \zeta $. Hence the two maps $ s\mapsto s $ and $s\mapsto\bar{s} $ are the symmetries of the multiset of non trivial zeroes of $ \zeta $. Adding a hypothetical zero off the line gives rise to the additional... | |
| Jan 8, 2018 at 11:00 | comment | added | bonif | Can you elaborate on this example or maybe give some reference where this result is explained or implied? | |
| S Oct 31, 2014 at 20:53 | history | answered | Sylvain JULIEN | CC BY-SA 3.0 | |
| S Oct 31, 2014 at 20:53 | history | made wiki | Post Made Community Wiki by Sylvain JULIEN |