Adrian Dudek

most citedOn Solving a Curious Inequality of Ramanujan

1 citations · 1 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2015

On the Distribution of Products of Primes and Powers

Adrian Dudek

We prove several results regarding the distribution of numbers that are the product of a prime and a $k$ -th power. First, we prove an asymptotic formula for the counting function o…

math.CO2015

Gaps Between Almost-Primes and a Construction of Almost-Ramanujan Graphs

Adrian Dudek

For all $k \geq 3$ , we show how one can explicitly construct an infinite family of $k$ -regular graphs all of which have second largest eigenvalue satisfying the bound $O (k^{1/2})$ .…

math.CO2014

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 $P (n, k)$ tends to zero as $n \to \infty$ . Moreover, we provide explicit upper b…

math.NT2014

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.

math.NT2014

An Explicit Result for $∣ L (1 + i t, χ) ∣$

Adrian Dudek

We give an explicit upper bound for non-principal Dirichlet $L$ -functions on the line $s = 1 + i t$ . This result can be applied to improve the error in the zero-counting formulae for th…

math.NT2014

Some Notes on Digit Strings in the Primes

Adrian Dudek

Let $S$ be a string of $l$ decimal digits. We give an explicit upper bound on some prime $p$ whose decimal representation contains the string $S$ . We also show, as a corollary of t…

On the Distribution of Products of Primes and Powers

Gaps Between Almost-Primes and a Construction of Almost-Ramanujan Graphs

On the Spectrum of the Generalised Petersen Graphs

On the Sum of a Prime and a Square-free Number

An Explicit Result for ∣L(1+it,χ)∣

Some Notes on Digit Strings in the Primes

An Explicit Result for $∣ L (1 + i t, χ) ∣$