The Zagier polynomials. Part II: Arithmetic properties of coefficients

2013/03/26 by Coffey, Mark W., De Angelis, Valerio, Dixit, Atul +3
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1303.6590

Abstract

The modified Bernoulli numbers B_n^* = ∑_r=0ⁿ \binomn+r2r \fracB_rn+r, n gt; 0 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.

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