The Riemann zeta function and tuning: Difference between revisions
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\zeta(s) = \sum_n n^{-s}</math> | \zeta(s) = \sum_n n^{-s}</math> | ||
Now let's do two things: we're going to expand {{nowrap|''s'' {{=}} σ + ''it''}}, and we're going to multiply ζ(s) by its conjugate ζ(''s'')′, noting that {{nowrap|ζ(''s'') | Now let's do two things: we're going to expand {{nowrap|''s'' {{=}} σ + ''it''}}, and we're going to multiply ζ(s) by its conjugate ζ(''s'')′, noting that {{nowrap|ζ(''s'')′ {{=}} ζ(''s''′)}} and {{nowrap|ζ(''s'') ⋅ ζ(''s'')′ {{=}} ζ(''s'')<sup>2</sup>}}. We get: | ||
<math> \displaystyle | <math> \displaystyle | ||