Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

A paper accepted by the Glasgow Mathematical Journal

A paper by Marina Avitabile (Univ. of Milano Bicocca) and Sandro Mattarei (Univ. of Lincoln), Generalized finite polylogarithms, has been accepted for publication in the Glasgow Mathematical Journal.

Abstract:
We introduce a generalization $\pounds_{d}^{(\alpha)}(X)$ of the finite polylogarithms $\pounds_{d}^{(0)}(X)=\pounds_d(X)=\sum_{k=1}^{p-1}X^k/k^d$, in characteristic $p$, which depends on a parameter $\alpha$.
The special case $\pounds_{1}^{(\alpha)}(X)$ was previously investigated by the authors as the inverse, in an appropriate sense, of a parametrized generalization of the truncated exponential which is instrumental in a grading switching technique for non-associative algebras. Here we extend such generalization to $\pounds_{d}^{(\alpha)}(X)$ in a natural manner, and study some properties satisfied by those polynomials. In particular, we find how the polynomials $\pounds_{d}^{(\alpha)}(X)$ are related to the powers of $\pounds_{1}^{(\alpha)}(X)$ and derive some consequences.

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This entry was posted on October 11, 2019 by in New publications, research.