7 citations · 21 across the 19 of their papers we have counts for
9 papers · 1 filter
On the Spectrum of the Generalised Petersen Graphs
Adrian Dudek
We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs tends to zero as . Moreover, we provide explicit upper b…
On the Sum of a Prime and a Square-free Number
Adrian Dudek
We prove that every integer greater than two may be written as the sum of a prime and a square-free number.
An Explicit Result for
Adrian Dudek
We give an explicit upper bound for non-principal Dirichlet -functions on the line . This result can be applied to improve the error in the zero-counting formulae for th…
Some Notes on Digit Strings in the Primes
Adrian Dudek
Let be a string of decimal digits. We give an explicit upper bound on some prime whose decimal representation contains the string . We also show, as a corollary of t…
On Solving a Curious Inequality of Ramanujan
Dave Platt, Adrian Dudek
Ramanujan proved that the inequality holds for all sufficiently large values of . Using an explicit estimate for the error i…
Almost-Ramanujan Graphs and Prime Gaps
Adrian Dudek
The method of Murty and Cioabă shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler constructio…
On the Riemann Hypothesis and the Difference Between Primes
Adrian Dudek
We prove some results concerning the distribution of primes on the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval $(x-\frac{4}π \…
An Explicit Result for Primes Between Cubes
Adrian Dudek
We prove that there is a prime between and for all . Our new tool which we derive is a version of Landau's explicit formula for the Riema…
An Elementary Proof of an Asymptotic Formula of Ramanujan
Adrian Dudek
We derive the mean square of the divisor function using only elementary techniques.