Hochschild homology, trace map and $\zeta$-cycles

Abstract

In this paper we consider two spectral realizations of the zeros of the Riemann zeta function. The first one involves all non-trivial (non-real) zeros and is expressed in terms of a Laplacian intimately related to the prolate wave operator. The second spectral realization affects only the critical zeros and it is cast in terms of sheaf cohomology. The novelty is that the base space is the Scaling Site playing the role of the parameter space for the $\zeta$-cycles and encoding their stability by coverings.

18 pages

References in corpus (23)

• Branching fractions, polarisation and asymmetries of B -> VV decays
• Measurement of the pseudoscalar mixing angle and ${\eta }^{\prime }$ gluonium content with KLOE detector
• Lattice Results for Low Moments of Light Meson Distribution Amplitudes
• Updating B --> PP, VP decays in the framework of flavor symmetry
• Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing
• Penguin-dominated B -> PV decays in NLO perturbative QCD
• Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes
• Improved Estimates of The $B_{(s)}\to VV$ Decays in Perturbative QCD Approach
• Charmless Two-body $B(B_s)\to VP$ decays In Soft-Collinear-Effective-Theory
• New physics in $B$ meson mixing: future sensitivity and limitations
• Next-to-leading-order corrections to exclusive processes in $k_T$ factorization
• Implication of the B -> rho rho data on the B -> pi pi puzzle
• Global Analysis of Charmless $B$ Decays into Two Vector Mesons in Soft-Collinear Effective Theory
• Glauber gluons in spectator amplitudes for $B\to \pi M$ decays
• $B\to \pi \pi$ decays and effects of the next-to-leading order contributions
• Next-to-leading-order time-like pion form factors in $k_T$ factorization
• Branching Ratio and CP Asymmetry of $B^0\to {\eta }^{(\prime )}{\eta }^{(\prime )}$ Decays in the Perturbative QCD Approach
• Transverse-momentum-dependent wave functions with Glauber gluons in $B\to \pi \pi$, $\rho \rho$ decays
• Study of $B_{(s)}\to (\pi \pi )(K\pi )$ decays in the perturbative QCD approach
• Reinvestigating the $B$ $\to$ $PP$ decays by including the contributions from ${\varphi }_{B2}$
• NLO contributions to $B\to K{K}^{\ast }$ Decays in the pQCD approach
• The NLO contributions to the scalar pion form factors and the $\mathcal{O}({\alpha }_s^2)$ annihilation corrections to the $B\to \pi \pi$ decays
• Resummation of Large Logarithms in ${\gamma }^{\ast }{\pi }^0\to \gamma$

Cited by in corpus (1)

• Estimates of the isospin-violating ${\Lambda }_b\to {\Sigma }^0\varphi ,{\Sigma }^{0}J/\psi$ decays and the $\Sigma -\Lambda$ mixing