In general I'm interested in representation theory, automorphic forms, analytic number theory. Recently I'm most interested in using the compact induction theory to study some analytic number theory problems like moments of L-functions, subconvexity bound, period integrals.
Papers
1. Cuspidal part of an eisenstein series restricted to an index 2 subfield. Research in Number Theory, 2(1):33, 2016.
2.Triple product formula and the subconvexity bound of triple product l-function in level aspect. American Journal of Mathematics, 139(1):215-259, 2017.
3. Triple product formula and mass equidistribution on modular curves of level N. IMRN, (9):2899-2943, 2018.
4. Some analytic aspects of automorphic forms on GL(2) of minimal type. Joint work with P. Nelson and A. Saha. Comment. Math. Helv. 94 (2019), no. 4, 767–801.
5. Test vectors for Waldspurger’s period integral and application to the mass equidistribution on nonsplit torus. arXiv:1608.06106.
Later improvement: Mass equidistribution on the torus in the depth aspect. Algebra & Number Theory 14-4 (2020), 927--946. DOI 10.2140/ant.2020.14.927 .
6. Sup norm on PGLn in depth aspect. arXiv:1809.00617.
7. An explicit gross-zagier formula related to the sylvester conjecture. Joint work with H. Yin and J. Shu. Trans. Amer. Math. Soc. 372 (2019), no. 10, 6905–6925.
8. Waldspurger's period integral for newforms. Joint work with H. Yin and J. Shu. Acta Arith. 195 (2020), no. 2, 177–197.
9. New test vector for Waldspurger’s period integral. Joint work with P. Nelson. arXiv:1810.11564.
10. Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II. Joint work with A. Saha. Compositio Mathematica , 156(2020) , Vol.11, 2368 - 2398
DOI: https://doi.org/10.1112/S0010437X20007460
11. The Petersson/Kuznetsov trace formula with prescribed local ramifications . American Journal of Mathematics, Vol.146, No.5, October 2024, pp. 1193-1252.
12. The subconvexity problem for Rankin-Selberg and triple product L-functions. Joint work with P. Michel and P. Nelson. arXiv:2207.14449.
13. Subconvex bounds for Un+1×Un in horizontal aspects. Joint work with P. Nelson. arXiv:2309.06314.
14. A generalized PGL(2) Petersson/Bruggeman/Kuznetsov formula for analytic applications. Joint work with I. Petrow and M. P. Young. arXiv:2411.05672.
15. The subconvexity bound for standard L-function in level aspect. Joint work with P.Nelson. arXiv:2503.12310 .
16.The cubic moment of L-functions for specified local component families. Joint work with I. Petrow and M. P. Young. arXiv:2506.14741