Spanning tree generating functions and Mahler measures
نویسندگان
چکیده
منابع مشابه
Higher Mahler measures and zeta functions
We consider a generalization of the Mahler measure of a multivariable polynomial P as the integral of log |P | in the unit torus, as opposed to the classical definition with the integral of log |P |. A zeta Mahler measure, involving the integral of |P |s, is also considered. Specific examples are computed, yielding special values of zeta functions, Dirichlet L-functions, and polylogarithms.
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The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures (1) m(y + 2xy + y − x − 2x − x) = 5 7 m(y + 4xy + y − x + x) , which is one of many examples that arise from the comparison of Mahler measures and special values of L-functions [Bo], [De], [RV]. Let us recall that the logarithmic Mahler measure of a Laurent polynomial P ∈ C[x 1 , . ...
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We investigate the set M∗ of numbers which occur as Mahler measures of integer polynomials and the subset M of Mahler measures of algebraic numbers (that is, of irreducible integer polynomials). We prove that every number α of degree d in M∗ is the Mahler measure of a separable integer polynomial of degree at most ∑ 1≤r≤d/2 ( d r ) with all its roots lying in the Galois closure F of Q(α), and e...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2012
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/45/49/494001