The Riemann zeta function and tuning: Difference between revisions

Line 94:

Note that for one of its neighbors, 271, it isn't entirely clear which peak value corresponds to the line of real values from +∞. This can be determined by looking at the absolute value of zeta along other ''s'' values, such as {{nowrap|''s'' {{=}} 1}} or {{nowrap|''s'' {{=}} {{frac|3|4}}}}, and in this case the local minimum at 271.069 is the value in question. However, other peak values are not without their interest; the local maximum at 270.941, for instance, is associated to a different mapping for 3.

To generate this plot using the free version of Wolfram Cloud, you can ~~copy-paste~~ <code>Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9, 12.1}]</code> and then in the menu select '''Evaluation > Evaluate Cells'''. Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".

To generate this plot using the free version of Wolfram Cloud, you can run <code>Plot{{!(}}Abs{{!(}}RiemannSiegelZ{{!(}}9.06472028x{{))!}}, {{(}}x, 11.9, 12.1{{)}}{{)!}}</code> and then in the menu select '''Evaluation > Evaluate Cells'''. Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".

You can also view the plot using [https://www.desmos.com/calculator/dstp7wnidf Zeta in Desmos].

@@ Line 94: / Line 94: @@
 Note that for one of its neighbors, 271, it isn't entirely clear which peak value corresponds to the line of real values from +∞. This can be determined by looking at the absolute value of zeta along other ''s'' values, such as {{nowrap|''s'' {{=}} 1}} or {{nowrap|''s'' {{=}} {{frac|3|4}}}}, and in this case the local minimum at 271.069 is the value in question. However, other peak values are not without their interest; the local maximum at 270.941, for instance, is associated to a different mapping for 3.
-To generate this plot using the free version of Wolfram Cloud, you can copy-paste <code>Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9, 12.1}]</code> and then in the menu select '''Evaluation &gt; Evaluate Cells'''. Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".
+To generate this plot using the free version of Wolfram Cloud, you can run <code>Plot{{!(}}Abs{{!(}}RiemannSiegelZ{{!(}}9.06472028x{{))!}}, {{(}}x, 11.9, 12.1{{)}}{{)!}}</code> and then in the menu select '''Evaluation &gt; Evaluate Cells'''. Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".
 You can also view the plot using [https://www.desmos.com/calculator/dstp7wnidf Zeta in Desmos].