We present a theoretical study of the static and dynamical properties of the three-dimensional, hyperhoneycomb Kitaev magnet β-Li2IrO3. We argue that the observed incommensurate order can be understood in terms of a long-wavelength twisting of a nearby commensurate period-3 state, with the same key qualitatively features. The period-3 state shows very different structure when either the Kitaev interaction K or the off-diagonal exchange anisotropy Γ is dominant. A comparison of the associated static spin structure factors with reported scattering experiments in zero and finite fields gives strong evidence that β-Li2IrO3 lies in the regime of dominant Kitaev coupling, and that the Heisenberg exchange J is much weaker than both K and Γ. Our predictions for the magnon excitation spectra, the dynamical spin structure factors, and their polarization dependence provide additional distinctive fingerprints that can be checked experimentally.
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We are especially grateful to Radu Coldea for several fruitful comments and suggestions and for pointing out the close connection of our results to the recent scattering experiments in finite fields  . We are also grateful to Cristian Batista, Eunsong Choi, Pavel Maksimov, Yuriy Sizyuk, and Alexander Tsirlin for valuable discussions. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0018056.