The Berry-Keating Hamiltonian and the Local Riemann Hypothesis

Details The Berry-Keating Hamiltonian and the Local Riemann Hypothesis The Berry-Keating Hamiltonian and the Local Riemann Hypothesis

2011-04-11

arxiv.org/abs/1104.1850v3

J. Phys. A 44, 305202 (2011) [IOP Select]

Physics

Mathematical Physics

9 pages, no figures; v2 included more mathematical background, v3 has minor edits for clarity

Scientific paper

The local Riemann hypothesis states that the zeros of the Mellin transform of a harmonic-oscillator eigenfunction (on a real or p-adic configuration space) have real part 1/2. For the real case, we show that the imaginary parts of these zeros are the eigenvalues of the Berry-Keating hamiltonian H=(xp+px)/2 projected onto the subspace of oscillator eigenfunctions of lower level. This gives a spectral proof of the local Riemann hypothesis for the reals, in the spirit of the Hilbert-Polya conjecture. The p-adic case is also discussed.

Affiliated with

Also associated with

No associations

Rating

The Berry-Keating Hamiltonian and the Local Riemann Hypothesis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Berry-Keating Hamiltonian and the Local Riemann Hypothesis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Berry-Keating Hamiltonian and the Local Riemann Hypothesis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-58128