12 citations · 55 across the 18 of their papers we have counts for
21 papers
On the finiteness of Bernoulli polynomials whose derivative has only integral coefficients
Bernd C. Kellner
It is well known that the Bernoulli polynomials have nonintegral coefficients for . However, ten cases are known so far in which the derivative $\mathbf…
On the nonintegrality of certain generalized binomial sums
Bernd C. Kellner
We consider certain generalized binomial sums and discuss the nonintegrality of their values for integral parameters and $\ell \in \mathbb{…
On (self-) reciprocal Appell polynomials: Symmetry and Faulhaber-type polynomials
Bernd C. Kellner
The main purpose of this paper is to study generalized (self-) reciprocal Appell polynomials, which play a certain role in connection with Faulhaber-type polynomials. More precisel…
Shifted sums of the Bernoulli numbers, reciprocity, and denominators
Bernd C. Kellner
We consider the numbers (in umbral notation with the Bernoulli numbers) that have a well-known rec…
Faulhaber polynomials and reciprocal Bernoulli polynomials
Bernd C. Kellner
About four centuries ago, Johann Faulhaber developed formulas for the power sum in terms of . The resulting polynomials are called the Faulhabe…
On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base- digits
Bernd C. Kellner, Jonathan Sondow
We give a new characterization of the set of Carmichael numbers in the context of -adic theory, independently of the classical results of Korselt and Carmichael. T…