Abstract
We relate poles of local Godement–Jacquet L-functions to distributions on matrix spaces with singular supports. As an application, we show the irreducibility of the full theta lifts to \({\mathrm {GL}}_n({\mathrm {F}})\) of generic irreducible representations of \({\mathrm {GL}}_n({\mathrm {F}})\), where \({\mathrm {F}}\) is an arbitrary local field.
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Acknowledgements
B. Sun would like to thank Jiajun Ma and Wee Teck Gan for helpful discussions. Y. Fang was supported in part by the National Natural Science Foundation of China (no. 11601341), and the National Key Research and Development Program of China (no. 2016QY04W0805). B. Sun was supported in part by the National Natural Science Foundation of China (nos. 11525105, 11688101, 11621061 and 11531008).
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Fang, Y., Sun, B. & Xue, H. Godement–Jacquet L-functions and full theta lifts. Math. Z. 289, 593–604 (2018). https://doi.org/10.1007/s00209-017-1967-z
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DOI: https://doi.org/10.1007/s00209-017-1967-z