K. Dilcher

activity

20182026

most citedHankel Determinants of sequences related to Bernoulli and Euler Polynomials

4 citations · 6 across the 16 of their papers we have counts for

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Showing 2019Show all

3 papers · 1 filter

math.NT2019

Arithmetic properties of polynomial solutions of the Diophantine equation $P (x) x^{n + 1} + Q (x) (x + 1)^{n + 1} = 1$

Karl Dilcher, Maciej Ulas

For each integer $n \geq 1$ we consider the unique polynomials $P, Q \in Q [x]$ of smallest degree $n$ that are solutions of the equation $P (x) x^{n + 1} + Q (x) (x + 1)^{n + 1} = 1$ . We d…

math.NT2019

Polynomial analogues of restricted multicolor b-ary partition functions

Karl Dilcher, Larry Ericksen

Given an integer base $b \geq 2$ , a number $ρ \geq 1$ of colors, and a finite sequence $Λ = (λ_{1}, \dots, λ_{ρ})$ of positive integers, we introduce the concept of a $Λ$ -restricted $ρ$ -col…

math.NT2019

Identities for Bernoulli polynomials related to multiple Tornheim zeta functions

Karl Dilcher, Armin Straub, Christophe Vignat

We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order co…

Arithmetic properties of polynomial solutions of the Diophantine equation P(x)xn+1+Q(x)(x+1)n+1=1

Polynomial analogues of restricted multicolor b-ary partition functions

Identities for Bernoulli polynomials related to multiple Tornheim zeta functions

Arithmetic properties of polynomial solutions of the Diophantine equation $P (x) x^{n + 1} + Q (x) (x + 1)^{n + 1} = 1$