S. Heintze

activity

20192026

most citedOn the growth of linear recurrences in function fields

6 citations · 33 across the 18 of their papers we have counts for

collaborators

18 papers

math.NT2026

On the asymptotic average diameter of blocks of uniformly distributed sequences and related results

Sebastian Heintze, Wolfgang Trutschnig

This paper was triggered by recent results on the maximal `average distance between consecutive points' of uniformly distributed sequences (u.f.d.s.). Here we address a generalized…

math.NT2025

Decidability of multiplicative matrix equations and related Diophantine problems

Sebastian Heintze, Armand Noubissie, Robert F. Tichy

Some new decidability results for multiplicative matrix equations over algebraic number fields are established. In particular, special instances of the so-called knapsack problem a…

math.NT2023★ 1 cited

On Pillai's Problem involving Lucas sequences of the second kind

Sebastian Heintze, Volker Ziegler

In this paper we consider the Diophantine equation $V_{n} - b^{m} = c$ for given integers $b, c$ with $b \geq 2$ , whereas $V_{n}$ varies among Lucas-Lehmer sequences of the second…

math.NT2022★ 2 cited

On the Diophantine equation $U_{n} - b^{m} = c$

Sebastian Heintze, Robert F. Tichy, Ingrid Vukusic +1

Let $(U_{n})_{n \in N}$ be a fixed linear recurrence sequence defined over the integers (with some technical restrictions). We prove that there exist effectively computable c…

math.NT2022

On the size of a linear combination of two linear recurrence sequences over function fields

Sebastian Heintze

Let $G_{n}$ and $H_{m}$ be two non-degenerate linear recurrence sequences defined over a function field $F$ in one variable over $C$ , and let $μ$ be a valuation on $…

math.NT2022★ 1 cited

On the growth of multi-recurrences

Clemens Fuchs, Sebastian Heintze

In this paper we provide a complete proof for a bound on the growth of multi-recurrences which are defined over a number field. The proven bound was already stated by van der Poort…

math.NT2022

Pillai's conjecture for polynomials

Sebastian Heintze

In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation \begin{equation*} p^n - q^m = f. \end{equation*} We prove that for any…

math.NT2021

Asymptotics for Pillai's problem with polynomials

Sebastian Heintze

Let $a_{1} (x) p_{1} (x)^{n} + \dots + a_{k} (x) p_{k} (x)^{n}$ as well as $b_{1} (x) q_{1} (x)^{m} + \dots + b_{l} (x) q_{l} (x)^{m}$ be two polynomial power sums where the complex polynomials $p_{i} (x)$ and…

math.NT2021

$S$ -unit values of $G_{n} + G_{m}$ in function fields

Sebastian Heintze

In this paper we consider a simple linear recurrence sequence $G_{n}$ defined over a function field in one variable over the field of complex numbers. We prove an upper bound on th…

math.NT2021★ 2 cited

Approximation of values of algebraic elements over the ring of power sums

Clemens Fuchs, Sebastian Heintze

Let $Q E_{Z}$ be the set of power sums whose characteristic roots belong to $Z$ and whose coefficients belong to $Q$ , i.e. $ G :…

math.NT2020

Diophantine equations in separated variables and polynomial power sums

Clemens Fuchs, Sebastian Heintze

We consider Diophantine equations of the shape $f (x) = g (y)$ , where the polynomials $f$ and $g$ are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we…

math.NT2020★ 6 cited

A function field variant of Pillai's problem

Clemens Fuchs, Sebastian Heintze

In this paper, we consider a variant of Pillai's problem over function fields $F$ in one variable over $C$ . For given simple linear recurrence sequences $G_{n}$ and $…

math.NT2020★ 5 cited

Integral zeros of a polynomial with linear recurrences as coefficients

Clemens Fuchs, Sebastian Heintze

Let $K$ be a number field, $S$ a finite set of places of $K$ , and $O_{S}$ be the ring of $S$ -integers. Moreover, let $$ G_n^{(0)} Z^d + \cdots + G_n^{(d-1)} Z + G…

math.NT2020★ 3 cited

A Polynomial Variant of Diophantine Triples in Linear Recurrences

Clemens Fuchs, Sebastian Heintze

Let $(G_{n})_{n = 0}^{\infty}$ be a polynomial power sum, i.e. a simple linear recurrence sequence of complex polynomials with power sum representation $ G_n = f_1α_1^n + \cdots + f_…

math.NT2020★ 4 cited

Norm form equations with solutions taking values in a multi-recurrence

Clemens Fuchs, Sebastian Heintze

We are interested in solutions of a norm form equation that takes values in a given multi-recurrence. We show that among the solutions there are only finitely many values in each c…

math.NT2020★ 6 cited

On the growth of linear recurrences in function fields

Clemens Fuchs, Sebastian Heintze

Let $(G_{n})_{n = 0}^{\infty}$ be a non-degenerate linear recurrence sequence with power sum representation $G_{n} = a_{1} (n) α_{1}^{n} + \dots + a_{t} (n) α_{t}^{n}$ . In this paper we will prov…

math.NT2019★ 3 cited

Perfect powers in polynomial power sums

Clemens Fuchs, Sebastian Heintze

We prove that a non-degenerate simple linear recurrence sequence $(G_{n} (x))_{n = 0}^{\infty}$ of polynomials satisfying some further conditions cannot contain arbitrary large powers…

math.NT2019

Yet another $S$ -unit variant of Diophantine tuples

Clemens Fuchs, Sebastian Heintze

We show that there are only finitely many triples of integers $0 < a < b < c$ such that the product of any two of them is the value of a given polynomial with integer coefficient…

On the asymptotic average diameter of blocks of uniformly distributed sequences and related results

Decidability of multiplicative matrix equations and related Diophantine problems

On Pillai's Problem involving Lucas sequences of the second kind

On the Diophantine equation Un​−bm=c

On the size of a linear combination of two linear recurrence sequences over function fields

On the growth of multi-recurrences

Pillai's conjecture for polynomials

Asymptotics for Pillai's problem with polynomials

S-unit values of Gn​+Gm​ in function fields

Approximation of values of algebraic elements over the ring of power sums

Diophantine equations in separated variables and polynomial power sums

A function field variant of Pillai's problem

Integral zeros of a polynomial with linear recurrences as coefficients

A Polynomial Variant of Diophantine Triples in Linear Recurrences

Norm form equations with solutions taking values in a multi-recurrence

On the growth of linear recurrences in function fields

Perfect powers in polynomial power sums

Yet another S-unit variant of Diophantine tuples

On the Diophantine equation $U_{n} - b^{m} = c$

$S$ -unit values of $G_{n} + G_{m}$ in function fields

Yet another $S$ -unit variant of Diophantine tuples