Mahler Measures as Linear Combinations of L–values of Multiple Modular Forms
نویسندگان
چکیده
منابع مشابه
The values of Mahler measures
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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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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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2015
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2014-012-8