Research Areas: Number Theory and Related Fields, including automorphic forms, elliptic curves, BSD 

          conjecture and Goldfeld’s conjecture et al.

  zhai@sdu.edu.cn

2005-2015 BA and PhD in Mathematics, Shandong University, Supervisor: Professor Jianya Liu

2012-2015 Joint PhD in Mathematics, University of Cambridge, Supervisor: Professor John Coates

2015-2017 Assistant Professor, Shandong University

2017-2021 Postdoc and Research Fellow, University of Cambridge

2021-     Professor, Shandong University

·Quadratic forms, K-groups and L-values of elliptic curves. Submitted, 2023. With L. Deng and Y. Li.

·Integral power sums of Hecke eigenvalues over quadratic forms. Submitted, 2022. With W. Zhao.  

·Elliptic curves with complex multiplication and the 2-part of the Birch and Swinnerton-Dyer conjecture. Preprint, 2022. With J. Coates.

·Generalized Birch lemma and the 2-part of the Birch and Swinnerton-Dyer conjecture for certain elliptic curves. J. reine angew. Math. 775 (2021), 117--143. With J. Shu.

·The Birch--Swinnerton-Dyer exact formula for quadratic twists of elliptic curves. Submitted, 2021.

·A lower bound result for the central L-values of elliptic curves. J. Number Theory 207 (2020), 356--366.

·On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture. Math. Proc. Cambridge Philos. Soc. 168 (2020), no. 1, 197--209.

·On the 2-part of the Birch and Swinnerton-Dyer conjecture for quadratic twists of elliptic curves. J. Lond. Math. Soc. (2) 101 (2020), no. 2, 714--734. With L. Cai and C. Li.

·Non-vanishing theorems for quadratic twists of elliptic curves. Asian J. Math. 20 (2016), no. 3, 475--502.

·Quadratic twists of elliptic curves. Proc. Lond. Math. Soc. (3) 110 (2015), no. 2, 357--394. With J. Coates, Y. Li and Y. Tian.

·Average behavior of Fourier coefficients of cusp forms over sum of two squares. J. Number Theory 133 (2013), no. 11, 3862--3876.

·Estimates of generalized Chebyshev function on GLm. Front. Math. China 7 (2012), no. 5, 883--894. With Y. Qu.