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Digital planar holography enables the creation of a new generation of integrated photonic circuits with desired transfer function. We give here, for the first time, the basis for designing computer-generated planar holograms and demonstrate their application for spectroscopy-on-chip. Nanospectrometer chips are demonstrated with unmatched spectral resolution of up to 2 ·105. A specific configuration is demonstrated for easy integration of planar holograms into the full spectrometer system. The ultraminiaturization and very high performances of the devices are a breakthrough in spectroscopy and open a novel route for the digital processing of light.