Timeline for The Riemann zeta function and differential operators
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 5 at 22:14 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Removed erroneous statement about a signed, masked Pascal triangle
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| Jan 16, 2021 at 21:39 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Elaborated on raising op
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| Jan 16, 2021 at 21:27 | comment | added | Tom Copeland | Uncorrect is incorrect, in both senses. | |
| Jan 16, 2021 at 21:26 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Corrected notation, added dJ(x)/dx
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| Jan 11, 2021 at 8:44 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Added another operator and link to applications of the Todd operator
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| Sep 17, 2019 at 23:12 | comment | added | reuns | It is uncorrect | |
| Sep 17, 2019 at 22:59 | comment | added | Tom Copeland | I@reuns I mean exactly what I derive in my blog post that I linked to. The pdf file does present Dirichlet series as well, but they aren't central to the discussion per se. If there is a spot in the analysis you don't follow, please point it out. The Mellin transform and the diff op derivations are pretty straightforwardly based on manipulations of Euler's product formula. | |
| Sep 17, 2019 at 20:13 | comment | added | reuns | You meant $\exp(-D_x\log n) \delta(x) = \sum_{k=0}^\infty \frac{(-\log n)^k}{k!} \delta^{(k)}(x)=\delta(x-\log n)$ in the sense of analytic functionals, with a convergent Dirichlet series $F(s)=\sum_{n=1}^\infty a_n n^{-s}$ then $ F(D_x)\delta = \sum_{n=1}^\infty a_n \exp(-D_x\log n)\delta$ converges in the sense of analytic functionals acting on bounded analytic functions and it is $ = \sum_{n=1}^\infty a_n \delta(x-\log n)$ which is the inverse Laplace transform of $F(s)$ in the sense of distributions. | |
| Sep 17, 2019 at 19:42 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Added raising operators
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| Sep 17, 2019 at 2:51 | history | asked | Tom Copeland | CC BY-SA 4.0 |