**The Zagier polynomials. Part II: arithmetic properties of coefficients**

Mark W. Coffey, Valerio De Angelis, Atul Dixit, Victor H. Moll, Armin Straub, Christophe Vignat — The Ramanujan Journal — Volume 35, Number 3, 2014, Pages 361-390

## 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 \(B_{r}\) by the Bernoulli polynomials \(B_{r}(x)\). 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.## Download

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## BibTeX

@article{bernoullizagier-2014, author = {Mark W. Coffey and Valerio De Angelis and Atul Dixit and Victor H. Moll and Armin Straub and Christophe Vignat}, title = {The {Z}agier polynomials. {Part II}: arithmetic properties of coefficients}, journal = {The Ramanujan Journal}, year = {2014}, volume = {35}, number = {3}, pages = {361--390}, doi = {10.1007/s11139-014-9568-5}, }