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math.NT2013
Rademacher-Carlitz Polynomials
Matthias Beck, Florian Kohl
We introduce and study the \emph{Rademacher-Carlitz polynomial} \[ \RC(u, v, s, t, a, b) := \sum_{k = \lceil s \rceil}^{\lceil s \rceil + b - 1} u^{\fl{\frac{ka + t}{b}}} v^k \] wh…
math.NT2013
Relations for Bernoulli--Barnes Numbers and Barnes Zeta Functions
Abdelmejid Bayad, Matthias Beck
The \emph{Barnes -function} is \[ ζ_n (z, x; \a) := \sum_{\m \in \Z_{\ge 0}^n} \frac{1}{\left(x + m_1 a_1 + \dots + m_n a_n \right)^z} \] defined for and $\Re(z) >…