The Mahler Measure for Arbitrary Tori
نویسنده
چکیده
We consider a variation of the Mahler measure where the defining integral is performed over a more general torus. We focus our investigation on two particular polynomials related to certain elliptic curve E and we establish new formulas for this variation of the Mahler measure in terms of L′(E, 0).
منابع مشابه
HIGHER MAHLER MEASURE OF AN n-VARIABLE FAMILY
We prove formulas for the k-higher Mahler measure of a family of rational functions with an arbitrary number of variables. Our formulas reveal relations with multiple polylogarithms evaluated at certain roots of unity.
متن کاملDALD:-Distributed-Asynchronous-Local-Decontamination Algorithm in Arbitrary Graphs
Network environments always can be invaded by intruder agents. In networks where nodes are performing some computations, intruder agents might contaminate some nodes. Therefore, problem of decontaminating a network infected by intruder agents is one of the major problems in these networks. In this paper, we present a distributed asynchronous local algorithm for decontaminating a network. In mos...
متن کاملOn the Davenport-Mahler bound
We prove that the Davenport-Mahler bound holds for arbitrary graphs with vertices on the set of roots of a given univariate polynomial with complex coefficients. Introduction The Davenport-Mahler bound is a lower bound for the product of the lengths of the edges on a graph whose vertices are the complex roots of a given univariate polynomial P ∈ C[X], under certain assumptions. Its origins are ...
متن کاملA New Method for Obtaining Polylogarithmic Mahler Measure Formulas
Given a formula for the Mahler measure of a rational function expressed in terms of polylogarithms, we describe a new method that allows us to construct a rational function with 2 more variables and whose Mahler measure is still expressed in terms of polylogarithms. We use this method to exhibit three new examples of Mahler measure and higher Mahler measure formulas. One of them involves a sing...
متن کامل1 3 Fe b 20 07 Mahler measure under variations of the base group Oliver
We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lück-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of Mahler measures over finite groups, for example, in the classical case of the f...
متن کامل