Kleene stars of the plane, polylogarithms and symmetries
We extend the definition and construct several bases for polylogarithms LiT, where T are some series, recognizable by a finite state (multiplicity) automaton of alphabet1X={x0,x1}. The kernel of this new “polylogarithmic map” Li• is also characterized and provides a rewriting process which terminate...
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Veröffentlicht in: | Theoretical computer science 2019-12, Vol.800, p.52-72 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We extend the definition and construct several bases for polylogarithms LiT, where T are some series, recognizable by a finite state (multiplicity) automaton of alphabet1X={x0,x1}. The kernel of this new “polylogarithmic map” Li• is also characterized and provides a rewriting process which terminates to a normal form. We concentrate on algebraic and analytic aspects of this extension allowing index polylogarithms at non-positive multi-indices, by rational series and regularize polyzetas at non-positive multi-indices2. |
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ISSN: | 0304-3975 1879-2294 |
DOI: | 10.1016/j.tcs.2019.10.016 |