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X Demographics
Mendeley readers
Attention Score in Context
| Title |
Hamiltonian for the Zeros of the Riemann Zeta Function
|
|---|---|
| Published in |
Physical Review Letters, March 2017
|
| DOI | 10.1103/physrevlett.118.130201 |
| Pubmed ID | |
| Authors |
Carl M Bender, Dorje C Brody, Markus P Müller |
| Abstract |
A Hamiltonian operator H[over ^] is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of H[over ^] is 2xp, which is consistent with the Berry-Keating conjecture. While H[over ^] is not Hermitian in the conventional sense, iH[over ^] is PT symmetric with a broken PT symmetry, thus allowing for the possibility that all eigenvalues of H[over ^] are real. A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that H[over ^] is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true. |
X Demographics
The data shown below were collected from the profiles of 334 X users who shared this research output. Click here to find out more about how the information was compiled.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| United States | 52 | 16% |
| United Kingdom | 28 | 8% |
| Japan | 25 | 7% |
| Australia | 10 | 3% |
| Spain | 8 | 2% |
| Germany | 7 | 2% |
| Italy | 6 | 2% |
| Canada | 6 | 2% |
| Belgium | 4 | 1% |
| Other | 35 | 10% |
| Unknown | 153 | 46% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Members of the public | 204 | 61% |
| Scientists | 124 | 37% |
| Practitioners (doctors, other healthcare professionals) | 4 | 1% |
| Science communicators (journalists, bloggers, editors) | 2 | <1% |
Mendeley readers
The data shown below were compiled from readership statistics for 241 Mendeley readers of this research output. Click here to see the associated Mendeley record.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| United States | 3 | 1% |
| Germany | 2 | <1% |
| Switzerland | 1 | <1% |
| France | 1 | <1% |
| Hungary | 1 | <1% |
| Canada | 1 | <1% |
| United Kingdom | 1 | <1% |
| China | 1 | <1% |
| Luxembourg | 1 | <1% |
| Other | 0 | 0% |
| Unknown | 229 | 95% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Student > Ph. D. Student | 75 | 31% |
| Researcher | 51 | 21% |
| Student > Bachelor | 19 | 8% |
| Student > Master | 16 | 7% |
| Professor > Associate Professor | 13 | 5% |
| Other | 44 | 18% |
| Unknown | 23 | 10% |
| Readers by discipline | Count | As % |
|---|---|---|
| Physics and Astronomy | 151 | 63% |
| Mathematics | 20 | 8% |
| Computer Science | 7 | 3% |
| Chemistry | 7 | 3% |
| Engineering | 7 | 3% |
| Other | 20 | 8% |
| Unknown | 29 | 12% |
Attention Score in Context
This research output has an Altmetric Attention Score of 371. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 17 December 2023.
All research outputs
#86,820
of 25,834,578 outputs
Outputs from Physical Review Letters
#118
of 40,571 outputs
Outputs of similar age
#2,084
of 324,379 outputs
Outputs of similar age from Physical Review Letters
#3
of 557 outputs
Altmetric has tracked 25,834,578 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 99th percentile: it's in the top 5% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 40,571 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 14.0. This one has done particularly well, scoring higher than 99% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 324,379 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 99% of its contemporaries.
We're also able to compare this research output to 557 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 99% of its contemporaries.