The Zagier polynomials. Part II: Arithmetic properties of coefficients
Number Theory
2013-03-27 v1
Abstract
The modified Bernoulli numbers \begin{equation*} B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 \end{equation*} introduced by D. Zagier in 1998 were recently extended to the polynomial case by replacing by the Bernoulli polynomials . Arithmetic properties of the coefficients of these polynomials are established. In particular, the 2-adic valuation of the modified Bernoulli numbers is determined. A variety of analytic, umbral, and asymptotic methods is used to analyze these polynomials.
Cite
@article{arxiv.1303.6590,
title = {The Zagier polynomials. Part II: Arithmetic properties of coefficients},
author = {Mark W. Coffey and Valerio De Angelis and Atul Dixit and Victor H. Moll and Armin Straub and Christophe Vignat},
journal= {arXiv preprint arXiv:1303.6590},
year = {2013}
}