V. Ziegler

activity

20152026

U_{n} - b^{m} = c

2 citations · 6 across the 10 of their papers we have counts for

collaborators

Showing 2020Show all

5 papers · 1 filter

math.NT2020

On a variant of Pillai's problem with transcendental numbers

Robert Tichy, Ingrid Vukusic, Daodao Yang +1

In this paper, we study the asymptotic behaviour of the number of solutions $(m, n) \in N^{2}$ to the inequality $∣ α^{n} - β^{m} ∣ \leq x$ when $x$ tends to infinity. Here $α,…

math.NT2020

Finding all $S$ -Diophantine quadruples for a fixed set of primes $S$

Volker Ziegler

Given a finite set of primes $S$ and a $m$ -tuple $(a_{1}, \dots, a_{m})$ of positive, distinct integers we call the $m$ -tuple $S$ -Diophantine, if for each $1 \leq i < j \leq m$ the quantit…

math.NT2020

Integers representable as differences of linear recurrence sequences

Robert Tichy, Ingrid Vukusic, Daodao Yang +1

Let ${U_{n}}_{n \geq 0}$ and ${V_{m}}_{m \geq 0}$ be two linear recurrence sequences. We establish an asymptotic formula for the number of integers $c$ in the range $[- x, x]$ which…

math.NT2020

Integers representable as differences of linear recurrence sequences

Daodao Yang

Let ${U_{n}}_{n ⩾ 0}$ and ${G_{m}}_{m ⩾ 0}$ be two linear recurrence sequences defined over the integers. We establish an asymptotic formula for the number of integ…

math.NT2020

Irrationality of growth constants associated with polynomial recursions

Stephan Wagner, Volker Ziegler

We consider integer sequences that satisfy a recursion of the form $x_{n + 1} = P (x_{n})$ for some polynomial $P$ of degree $d > 1$ . If such a sequence tends to infinity, then it satis…

On a variant of Pillai's problem with transcendental numbers

Finding all S-Diophantine quadruples for a fixed set of primes S

Integers representable as differences of linear recurrence sequences

Integers representable as differences of linear recurrence sequences

Irrationality of growth constants associated with polynomial recursions

Finding all $S$ -Diophantine quadruples for a fixed set of primes $S$