Harmonic entropy: Difference between revisions
→Equivalence of exp-UHE and UHE for a \leq 2: latex typo |
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Bounding by <math>\max(n,d) < N</math> is the same as specifying that <math>j_n < N</math> and <math>j_d < N</math>. Doing so, we get | Bounding by <math>\max(n,d) < N</math> is the same as specifying that <math>j_n < N</math> and <math>j_d < N</math>. Doing so, we get | ||
<math>\displaystyle \mathcal{F}\left\{K(n)\right\}(t) = \sum_{1 | <math>\displaystyle \mathcal{F}\left\{K(n)\right\}(t) = \sum_{1\leq j_n, j_d<N} \left[ \frac{1}{{j_n}^{0.5 -i t}} \cdot \frac{1}{{j_d}^{0.5 + i t}} \right]</math> | ||
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so that the choice of <math>a</math> simply changes our choice of vertical slice of the Riemann zeta function. | so that the choice of <math>a</math> simply changes our choice of vertical slice of the Riemann zeta function. | ||
===Analytic Continuation of Unnormalized Harmonic Rényi Entropy=== | ===Analytic Continuation of Unnormalized Harmonic Rényi Entropy=== | ||