Geodesic
Some cases of Kudla’s modularity conjecture for unitary Shimura varieties
Forum of Mathematics, Sigma, Tome 10 (2022)

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We use the method of Bruinier–Raum to show that symmetric formal Fourier–Jacobi series, in the cases of norm-Euclidean imaginary quadratic fields, are Hermitian modular forms. Consequently, combining a theorem of Yifeng Liu, we deduce Kudla’s conjecture on the modularity of generating series of special cycles of arbitrary codimension for unitary Shimura varieties defined in these cases. 
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     author = {Jiacheng Xia},
     title = {Some cases of {Kudla{\textquoteright}s} modularity conjecture for unitary {Shimura} varieties},
     journal = {Forum of Mathematics, Sigma},
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Jiacheng Xia. Some cases of Kudla’s modularity conjecture for unitary Shimura varieties. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.26

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