Special zeta Mahler functions

Special zeta Mahler functions

We study the zeta Mahler function (ZMF, also zeta Mahler measure ), which is closely related to the Mahler measure . Here we discuss a family of ZMFs attached to the Laurent polynomials k + ( x 1 + x 1 - 1 ) ⋯ x r + x r - 1 , where k is real. We give explicit formulae, present examples and establish...

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Veröffentlicht in:Research in number theory 2022-06, Vol.8 (2), Article 29
1. Verfasser: Ringeling, Berend
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical analysis
Mathematics
Mathematics and Statistics
Number Theory
Polynomials
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Zusammenfassung:We study the zeta Mahler function (ZMF, also zeta Mahler measure ), which is closely related to the Mahler measure . Here we discuss a family of ZMFs attached to the Laurent polynomials k + ( x 1 + x 1 - 1 ) ⋯ x r + x r - 1 , where k is real. We give explicit formulae, present examples and establish properties for these ZMFs, such as an RH-type phenomenon. Further, we explore connections with the Mahler measure.
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-022-00326-9