P. Moree

activity

19992026

most citedConvoluted convolved Fibonacci numbers

24 citations · 285 across the 74 of their papers we have counts for

collaborators

Showing 2017Show all

5 papers · 1 filter

math.NT2017

Irregular behaviour of class numbers and Euler-Kronecker constants of cyclotomic fields: the log log log devil at play

Pieter Moree

Kummer (1851) and, many years later, Ihara (2005) both posed conjectures on invariants related to the cyclotomic field $Q (ζ_{q})$ with $q$ a prime. Kummer's conjecture concer…

math.NT2017★ 2 cited

Constrained ternary integers

Florian Luca, Pieter Moree, Robert Osburn +2

An integer $n$ is said to be ternary if it is composed of three distinct odd primes. In this paper, we asymptotically count the number of ternary integers $n \leq x$ with the const…

math.NT2017

On the discriminator of Lucas sequences

Bernadette Faye, Florian Luca, Pieter Moree

We consider the family of Lucas sequences uniquely determined by $U_{n + 2} (k) = (4 k + 2) U_{n + 1} (k) - U_{n} (k),$ with initial values $U_{0} (k) = 0$ and $U_{1} (k) = 1$ and $k \geq 1$ an arbitrary inte…

math.NT2017

Browkin's discriminator conjecture

Alexandru Ciolan, Pieter Moree

Let $q \geq 5$ be a prime and put $q^{*} = (- 1)^{(q - 1) /2} \cdot q$ . We consider the integer sequence $u_{q} (1), u_{q} (2), \dots,$ with $u_{q} (j) = (3^{j} - q^{*} (- 1)^{j}) /4$ . No term in this sequence is r…

math.NT2017★ 4 cited

Denominators of Bernoulli polynomials

Olivier Bordellès, Florian Luca, Pieter Moree +1

For a positive integer $n$ let $P_{n} = \prod_{s_{p} (n) \geq p} p,$ where $p$ runs over all primes and $s_{p} (n)$ is the sum of the base $p$ digits of $n$ . For all $n$ we prove th…