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Publications Influence

On the Riemann hypothesis and the difference between primes

- A. Dudek
- Mathematics
- 26 February 2014

We prove some results concerning the distribution of primes assuming the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval $(x-\frac{4}{\pi} \sqrt{x}...

15 3- PDF

On the sum of a prime and a square-free number

- A. Dudek
- Mathematics
- 27 October 2014

We prove that every integer greater than two may be written as the sum of a prime and a square-free number.

9 3- PDF

An Explicit Result for Primes Between Cubes

- A. Dudek
- Mathematics
- 17 January 2014

We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-function… Expand

12 2- PDF

ON THE NUMBER OF DIVISORS OF $n^{2}-1$

- A. Dudek
- Mathematics
- Bulletin of the Australian Mathematical Society
- 30 July 2015

We prove an asymptotic formula for the sum $\sum _{n\leq N}d(n^{2}-1)$, where $d(n)$ denotes the number of divisors of $n$. During the course of our proof, we also furnish an asymptotic formula for… Expand

8 1- PDF

On the Success of Mishandling Euclid's Lemma

- A. Dudek
- Mathematics
- 21 January 2016

Abstract We examine Euclid's lemma that if p is a prime number such that p |ab, then p divides at least one of a or b. Specifically, we consider the common misapplication of this lemma to numbers… Expand

2 1- PDF

Explicit Estimates in the Theory of Prime Numbers

- A. Dudek
- Mathematics
- 22 November 2016

It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers.
First, the problem of primes in short intervals is considered. We prove that… Expand

5 1- PDF

Comparison of Deep Tissue Massage and Therapeutic Massage for Lower Back Pain, Disease Activity, and Functional Capacity of Ankylosing Spondylitis Patients: A Randomized Clinical Pilot Study

- M. Romanowski, M. Špiritović, R. Rutkowski, A. Dudek, W. Samborski, A. Straburzyńska-Lupa
- Medicine
- Evidence-based complementary and alternative…
- 6 August 2017

Objectives This study aims to compare the effectiveness of deep tissue massage (DTM) and therapeutic massage (TM) in the management of ankylosing spondylitis (AS) patients. Materials and Methods This… Expand

6- PDF

On Solving a Curious Inequality of Ramanujan

- A. Dudek, D. J. Platt
- Computer Science, Mathematics
- Exp. Math.
- 7 July 2014

TLDR

5- PDF

Almost-Ramanujan graphs and prime gaps

- A. Dudek
- Computer Science, Mathematics
- Eur. J. Comb.
- 4 February 2014

The method of Murty and Cioab? shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the… Expand

2- PDF

Primes in explicit short intervals on RH

- A. Dudek, Loic Greni'e, G. Molteni
- Mathematics
- 24 February 2015

On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.

5- PDF