127 research outputs found
An algebraic integration for Mahler measure
There are many examples of several-variable polynomials whose Mahler measure
is expressed in terms of special values of polylogarithms. These examples are
expected to be related to computations of regulators, as observed by Deninger,
and later Rodriguez-Villegas, and Maillot. While Rodriguez-Villegas made this
relationship explicit for the two variable case, it is our goal to understand
the three variable case and shed some light on the examples with more
variables.Comment: 3 figure
On certain combination of colored multizeta values
We reduce the sum in terms of special values of the Dirichlet
L-series in the character of conductor 4. This sum is a combination of colored
zeta values
Mahler measure under variations of the base group
We study properties of a generalization of the Mahler measure to elements in
group rings, in terms of the Lueck-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 free abelian group or the infinite dihedral group, and others.Comment: 21 page
Higher Mahler measures and zeta functions
We consider a generalization of the Mahler measure of a multivariable
polynomial as the integral of in the unit torus, as opposed to
the classical definition with the integral of . A zeta Mahler measure,
involving the integral of , is also considered. Specific examples are
computed, yielding special values of zeta functions, Dirichlet -functions,
and polylogarithms
Biased statistics for traces of cyclic p-fold covers over finite fields
In this paper, we discuss in more detail some of the results on the statistics of the trace of the Frobenius endomorphism associated to cyclic p-fold covers of the projective line that were presented in [1]. We also show new findings regarding statistics associated to such curves where we fix the number of zeros in some of the factors of the equation in the affine model
Maritime satellite communications: its influence on maritime education & training and shipboard operations
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