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.

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