↓ Skip to main content

Hamiltonian for the Zeros of the Riemann Zeta Function

Overview of attention for article published in Physical Review Letters, March 2017
Altmetric Badge

About this Attention Score

  • In the top 5% of all research outputs scored by Altmetric
  • Among the highest-scoring outputs from this source (#40 of 26,324)
  • High Attention Score compared to outputs of the same age (99th percentile)
  • High Attention Score compared to outputs of the same age and source (99th percentile)

Citations

dimensions_citation
23 Dimensions

Readers on

mendeley
202 Mendeley
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.

Twitter Demographics

The data shown below were collected from the profiles of 398 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 202 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United States 4 2%
Switzerland 2 <1%
Germany 2 <1%
Luxembourg 1 <1%
United Kingdom 1 <1%
China 1 <1%
France 1 <1%
Hungary 1 <1%
Canada 1 <1%
Other 0 0%
Unknown 188 93%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 68 34%
Researcher 38 19%
Student > Bachelor 18 9%
Student > Master 15 7%
Unspecified 13 6%
Other 50 25%
Readers by discipline Count As %
Physics and Astronomy 136 67%
Unspecified 17 8%
Mathematics 16 8%
Computer Science 8 4%
Engineering 7 3%
Other 18 9%

Attention Score in Context

This research output has an Altmetric Attention Score of 410. 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 16 April 2019.
All research outputs
#22,637
of 12,961,968 outputs
Outputs from Physical Review Letters
#40
of 26,324 outputs
Outputs of similar age
#1,303
of 259,136 outputs
Outputs of similar age from Physical Review Letters
#5
of 641 outputs
Altmetric has tracked 12,961,968 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 26,324 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 11.0. 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 259,136 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 641 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.