Related papers: On Romanoff's theorem
We offer a generalization of a formula of Popov involving the Von Mangoldt function. Some commentary on its relation to other results in analytic number theory is mentioned as well as an analogue involving the m$\ddot{o}$bius function.
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.
We sketch several proofs of F\'ary--Milnor theorem.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
We extend some basic results known for finite range operators to long range operators with off-diagonal decay. Namely, we prove an analogy of Sch'nol's theorem. We also establish the connection between the almost sure spectrum of long range…
We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
An observation on Hall-Littlewood polynomials.
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
An technically interesting proof of a known theorem.
Computations in the cohomology of finite groups.
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
We prove Simon's conjecture for 3-manifolds.
The present study provides another look on Lamperti's theorem on recurrence or transience of stochastic sequences. We establish connection between Lamperti's theorem and the recent result by the author [V. M. Abramov, Theor. Probab. Math.…
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 will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.
We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.
We give some heuristic results for FRW situations with Ricci flow.
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
We prove some symmetric $q$-congruences.