The Riemann zeta function and tuning: Difference between revisions
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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 s=1 or s=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. | 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 s=1 or s=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 '''Plot[RiemannSiegelZ[9.06472028x], {x, 11.9,12.1}]''' 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 copy-paste '''Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9,12.1}]''' 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'''". | ||
= Mike Battaglia's Expanded Results = | = Mike Battaglia's Expanded Results = | ||