7 citations · 21 across the 19 of their papers we have counts for
5 papers · 1 filter
On the Number of Divisors of
Adrian Dudek
We prove an asymptotic formula for the sum , where denotes the number of divisors of . During the course of our proof, we also furnish an asym…
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 -th power. First, we prove an asymptotic formula for the counting function o…
On the Sum of the Square of a Prime and a Square-Free Number
Adrian Dudek, Dave Platt
We prove that every integer such that can be written as the sum of the square of a prime and a square-free number. This makes explicit a t…
Primes in explicit short intervals on RH
Adrian Dudek, Loïc Grenié, Giuseppe Molteni
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
Gaps Between Almost-Primes and a Construction of Almost-Ramanujan Graphs
Adrian Dudek
For all , we show how one can explicitly construct an infinite family of -regular graphs all of which have second largest eigenvalue satisfying the bound .…