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math.CA2026
Sharp rational points counting near nondegenerate curves in
Shengwen Gan, Shaoming Guo, Changkeun Oh
We establish sharp bounds for rational points near compact smooth nondegenerate curves in , for every . For a nondegenerate curve in …
math.AP2026
Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters
Shengwen Gan, Cheng Zhang, Zhifei Zhu
We prove sharp -linear estimates for Carleson--Sjölin oscillatory integral operators with arbitrary separated frequency scales for all and . The…