Related papers: Deep zero problems and the HRT conjecture
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
We survey results on Hedetniemi's conjecture which are connected to adjoint functors in the "thin" category of graphs, and expose the obstacles to extending these results.
Assume that the eigenvalues of a finite hermitian linear operator have been deduced accurately but the linear operator itself could not be determined with precision. Given a set of eigenvalues $\lambda$ and a hermitian matrix $M$, this…
We study decidability and complexity questions related to a continuous analogue of the Skolem-Pisot problem concerning the zeros and nonnegativity of a linear recurrent sequence. In particular, we show that the continuous version of the…
Based on the proof of Demeter \We prove that for almost every (1,3) configuration, there is no linear dependence between the associated time-frequency translates of any $f\in L^2(\R)\backslash \{0\}$.cite{Dem10}, we establish the HRT…
Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a…
Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|\zeta(1/2+it)|$ on the critical line, and zeros…
In this paper we consider two related objects: singular positive semidefinite Hankel block--matrices and associated degenerate truncated matrix Hamburger moment problems. The description of all solutions of a degenerate matrix Hamburger…
The Riemann Hypothesis is a conjecture that all non-trivial zeros of Riemann Zeta function are located on the critical line in the complex plane. Hundreds of propositions in function theory and analytic number theory rely on this…
The observed strong dark-to-luminous matter coupling suggests the existence of a some functional relation between visible and DM sources which leads to biased Einstein equations. We show that such a bias appears in the case when the…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
The classical Hermite-Biehler theorem describes possible zero sets of complex linear combinations of two real polynomials whose zeros strictly interlace. We provide the full characterization of zero sets for the case when this interlacing…
We consider deformations of quantum exterior algebras extended by finite groups. Among these deformations are a class of algebras which we call truncated quantum Drinfeld Hecke algebras in view of their relation to classical Drinfeld Hecke…
In 2009 Ekedahl introduced certain cohomological invariants of finite groups which are naturally related to the Noether Problem. We show that these invariants are trivial for every finite group in GL_3(k) and for the fifth discrete…
In this note, we attack a question posed ten years ago by Tsukiyama about the injectivity of the so- called Forgetable map. We show that we can insert the Forgetable map in an exact sequence and that the problem can be reduced to the…
We settle a conjecture of Farmer and Ki in a stronger form. Roughly speaking we show that there is a positive proportion of small gaps between consecutive zeros of the zeta-function $\zeta(s)$ if and only if there is a positive proportion…
Motivated by recent studies of the phenomenon of Coherent Perfect Absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as…
We study a new type of normal form at a critical point of an analytic Hamiltonian. Under a Bruno condition on the frequency, we prove a convergence statement to the normal form. Using this result, we prove the Herman invariant tori…
We associate a deformation of Heisenberg algebra to the suitably normalized Yang $R$-matrix and we investigate its properties. Moreover, we construct new examples of quantum vertex algebras which possess the same representation theory as…
A Hamiltonian operator $\hat H$ 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…