Generalized Thue-Morse sequences of squares
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We consider compact group generalizations T(n) of the Thue-Morse sequence and prove that the subsequence T(n 2) is uniformly distributed with respect to a measure gv that is absolutely continuous with respect to the Haar measure. The proof is based on a proper generalization of the Fourier based method of Mauduit and Rivat in their study of the sum-of-digits function of squares to group representations.
KeywordsNormal Subgroup Irreducible Representation Compact Group Unitary Representation Automatic Sequence
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