Related papers: Some assertions that are equivalent to Riemann hyp…
An equivalent formulation of the Riemann hypothesis is given. The physical interpretation of the Riemann hypothesis equivalent formulation is given in the framework of quantum theory terminology. One more power series related to the Riemann…
The Riemann hypothesis is identified with zeros of ${\cal N}=4$ supersymmetric gauge theory four-point amplitude. The zeros of the $\zeta(s)$ function are identified with th complex dimension of the spacetime, or the dimension of the…
Identities involving Mobius function values (u(j),u(k)) are used to generate a Riemann Hypothesis equivalent.
We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fourier integrals are provided.
We provide sufficient conditions on integrable analytic Hamiltonians that guarantee the existence, under arbitrary sufficiently small analytic perturbations, of invariant lower dimensional tori associated to an invariant resonant torus of…
Invariant torus are constructed under assumption that the homogeneous system admits an exponential dichotomy on the semi-axes. The main result is closely related with the well-known Palmer's lemma and results of Boichuk A.A., Samoilenko…
The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…
This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.
We extend Raimi's classical partition theorem to the continuous setting of the circle and $n$-dimensional torus. Building on recent work of Hegyv\'ari, Pach, and Pham in finite groups, we prove that there exist measurable partitions of the…
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
The paper presents several new sufficient conditions, as well as new equivalent criteria for the classical Riemann Hypothesis. Noteworthy are also other statements and remarks about $\zeta$ to be found throughout the paper.
We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-dimensional torus is unbounded. We provide explicit examples of Hamiltonian diffeomorphisms with arbitrarily large autonomous norm. For the proofs we…
Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.
An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the…
The conditions for convergence of square and rectangular Fejer means of functions on the infinite dimensional torus were obtained, also a generalization of the results for the case of abstract measure spaces was formulated.
Necessary and sufficient conditions for a Riemannian product to be conformally equivalent to an Einstein manifold are given. Such spaces which are complete are characterized.
This paper is a continuation of our recent paper with the same title, arXiv:0806.1596v1 [math.NT], where a number of integral equalities involving integrals of the logarithm of the Riemann zeta-function were introduced and it was shown that…
We provide various counter-examples to the long-standing so-called "Omnibus Conjecture" in Rational Homotopy Theory. That is, we show that a space with finite dimensional even-degree rational cohomology and finite dimensional spherical…
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity…