Related papers: A note on the Tikhonov theorem on an infinite inte…
In this short note, we establish an operator theoretic version of the Wiener-Ikehara tauberian theorem, and point out how this leads to a new proof of the Prime number theorem that should be accessible to anyone with a basic knowledge of…
The present note refers to a result proposed in [Elhadj and Sprott, 2012], and shows that the Theorem therein is not correct. We explain that a proof of that Theorem cannot be given, as the statement is not correct, and we underline a…
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
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.
In this short note we describe a simple but remarkably effective method for rigorously estimating Lyapunov exponents for expanding maps of the interval. We illustrate the applicability of this method with some standard examples.
We prove strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type. This gives another application of a previous trimming result only proven for interval maps. In case of Markov measures we…
We survey the classical results on the prime number theorem
This paper considers some infinite series involving the Riemann zeta function.
In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…
We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of…
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
In this short paper we review and extract some features of the Fredholm Alternative problem .
We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as using Hindman's theorem). This adds to the existing…
An equivalent but useful version on the Homological Nerve Theorem is proved.
We obtain simple proofs of certain inequalites for bivariate means.