We give an explicit formula for the twisted Koecher–Maaß series of the Duke–Imamoglu–Ikeda lift. As an application we prove a certain algebraicity result for the values of twisted Rankin–Selberg series at integers of half-integral weight modular forms, which was not treated by Shimura (J Math Soc Japan 33:649–672, 1981).
Explicit formulas for the twisted Koecher–Maaß series of the Duke–Imamoglu–Ikeda lift and their applications
twisted_KM_DII_arXiv_Muroran.pdf
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