American Mathematical Society, Proceedings of the American Mathematical Society, 1(146), p. 449-458, 2017
DOI: 10.1090/proc/13727
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As an application of Behrens and Rezk's spectral algebra model for unstable v_n-periodic homotopy theory, we give explicit presentations for the completed E-homology of the Bousfield-Kuhn functor on odd-dimensional spheres at chromatic level 2, and compare them to the level 1 case. The latter reflects earlier work in the literature on K-theory localizations.