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Motivated by the computations in the theory of cohomological Conley index, cocyclic subshifts are the supports of locally constant matrix cocycles on the full shift over a finite alphabet. They properly generalize sofic systems and topological Markov chains; and, via the Wedderburn-Artin theory...
In a recent joint work with V. Turaev , we defined a new concept of combinatorial torsion which we called absolute torsion. Compared with the classical Reidemeister torsion, it has the advantage of having a well-determined sign. Also, the absolute torsion is defined for arbitrary orientable...
In this paper we show by employing the Selberg trace formula that the
$t_j \log t_j$
are rather regularly distributed mod
(that is, we show that some degree of cancellation occurs) where
Given a Gelfand pair
is the Heisenberg group and K is a compact subgroup of the unitary group U(n) we consider the sphere and ball averages of certain K-invariant measures on
. We prove local ergodic theorems for these measures when
$n \geq 3$
. We also...
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