Special zeta Mahler functions
Copyright policy )Special zeta Mahler functions
AbstractWe 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 $$k + (x_1 + x_1^{-1}) \cdots \left( x_r + x_r^{-1}\right) $$ 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.
- Radboud University Nijmegen Netherlands
Mathematics - Number Theory, Mathematics - Complex Variables, FOS: Mathematics, 33C20, 33C60, 30D05, 30C15, 11R06, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Complex Variables (math.CV), Mathematics
Mathematics - Number Theory, Mathematics - Complex Variables, FOS: Mathematics, 33C20, 33C60, 30D05, 30C15, 11R06, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Complex Variables (math.CV), Mathematics
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