Related papers: Some assertions that are equivalent to Riemann hyp…

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…

We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex…

We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{\lambda_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we…

We estimate the energy and Hausdorff dimensions of the Riesz products on the unit sphere of $\mathbb{C}^n$, $n\ge 2$. Also, we obtain similar results for the pluriharmonic measures on the torus.

In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.

We prove several results concerning the discrepancy, tested on balls in the $d$-dimensional torus $\mathbb{T}^{d}$, between absolutely continuous measures and finite atomic measures.

It is proposed that the validity, or not, of the Riemann Hypothesis might be established on the basis of the integral $$\int\frac{\xi(2s)}{\xi(s)}ds$$ where $$\xi(s)=(s-1)\pi^{-s/2}\Gamma(1+s/2)\zeta(s).$$

Five geometrical eqivalents of Goldbach conjecture are given, calling one of them Fermat Like Theorem.

In this paper, we prove the Riemannian positive mass theorem up to dimension $19$, building on a combination of torical symmetrization and the singularity blow-up technique developed in [HSY26], together with the generic regularity theory…

In this paper, we give a connection between the Riemann hypothesis and uniqueness of the Riemann zeta function and an analogue for L-functions.

For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable…

The connection between multidimensional soliton equations and three-dimensional Riemann space is discussed.

Explicit formulas involving a generalized Ramanujan sum are derived. An analogue of the prime number theorem is obtained and equivalences of the Riemann hypothesis are shown. Finally, explicit formulas of Bartz are generalized.

We propose a model theoretic interpretation of the theorems about the equivalence between mixed characteristic perfectoid spaces and their tilts.

In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…

Several methods are used to evaluate finite trigonometric sums. In each case, either the sum had not previously been evaluated, or it had been evaluated, but only by analytic means, e.g., by complex analysis or modular transformation…

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

Conditions, related to Kulkarni's equivalence problem are considered for indefinite Riemannian and Kaehlerian manifolds. Corresponding theorems are obtained for the values of the Ricci tensor on isotropic vectors as well as for the values…

We find some statements in the language of asymmetric topology and continuous partial orders which are equivalent to the statements $\kappa < \mathfrak m$ or $\kappa < \mathfrak p$.