Timeline for Riemann Z function, bounds on number of non-trivial zeros along horizontal lines, rather than vertical ones
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 8, 2013 at 8:00 | comment | added | Luca | and whose number cannot exceed said already known limits you recalled. It is anyway a better estimate than simply relying on the fact that the zero set of a non-constant holomorphic function on a connected open set is discrete. | |
| Mar 27, 2013 at 8:43 | comment | added | Luca | Micah, thank you for those references. So, it appears that the consensus is that, for a horizontal line at height T, no stricter bounds are available than those already known for the number of zeros inside a rectangle corresponding to the critical strip up to height T. But thanks for pointing out that that is already sufficient to at least show that along said horizontal lines there cannot lie more than at most finitely many zeros (I had missed that now obvious implication ...). | |
| Mar 26, 2013 at 19:25 | comment | added | Marc Palm | I feel that bounds for the multiplicity of zeros is a more reasonable question, because we expect RH to be true. | |
| Mar 26, 2013 at 19:18 | history | edited | Marc Palm | CC BY-SA 3.0 |
added 108 characters in body
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| Mar 26, 2013 at 19:01 | history | answered | Marc Palm | CC BY-SA 3.0 |