Related papers: On Romanoff's theorem

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

We prove a result on the existence of linear forms of a given Diophantine type.

A proposed solution to the Riemann Hypothesis

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We generalize Rado's extension theorem to complex spaces.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

An equivalent but useful version on the Homological Nerve Theorem is proved.

We present several results, including some remarks on the Hopf Lemma.

We survey recent developments on the Restriction conjecture.

We improve constants in the Rademacher-Menchov inequality.

In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.

We prove a variation of Gronwall's lemma.

We prove an improved form of an expectation of Polya and discuss several related questions

We derive a number of extremal and Ramsey stability results for cycles.

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

In this note, we disprove two Romanov type conjectures posed by Chen.

In this article we give a result obtained of an experimental way for the Euler totient function.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

Via a functor from certain Lorentzian to Riemannian manifolds, we obtain a finiteness result.

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…