Abstract
In Kim [7], we studied an Eisenstein series on quaternion half-space of degree 2. By calculating the Siegel series using the method of Karel [5], we obtained the analytic continuation and functional equation of the Eisenstein series. In this note we study an Eisenstein series on quaternion half-space of degreen. By calculating the Siegel series in an analogous way as in Shimura [15] and Kitaoka [8], we obtain singular modular forms of weightk, k<2n and 4/k. Furthermore, we obtain the analytic continuation and functional equation of the Eisenstein series.
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Kim, H.H. Eisenstein series on quaternion half-space of degree N. Manuscripta Math 77, 215–235 (1992). https://doi.org/10.1007/BF02567055
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DOI: https://doi.org/10.1007/BF02567055