研究领域：数论及其相关领域，具体包括自守形式、椭圆曲线、BSD猜想、Goldfeld猜想等。

  

  zhai@sdu.edu.cn

 

 

2005-2009 山东大学 数学学院学士

2009-2015 山东大学 数学学院博士 导师刘建亚教授

2012-2015 剑桥大学 数学科学中心联培博士 导师John Coates教授

2015-2017 山东大学 高等研究院 助理研究员

2017-2021 剑桥大学 数学科学中心 博士后研究员

2021-至今 山东大学 数学与交叉科学研究中心 教授

·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.