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Special zeta Mahler functions

Special zeta Mahler functions

Abstract 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 $$k + (x_1 + x_1^{-1}) \cdots \left( x_r + x_r^{-1}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>+</mml:mo> …