**Shuai Zhai**

I am a Professor at Shandong University. I was formerly a Research Fellow of the Number Theory Group at University of Cambridge. My research interests include modular and automorphic forms, elliptic curves, and in particular, the Birch and Swinnerton-Dyer conjecture.

*Papers*

[9] 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.

[8] The Birch--Swinnerton-Dyer exact formula for quadratic twists of elliptic curves. Preprint.

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

[6] 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.

[5] 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.

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

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

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

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

*Address*

Institute for Advanced Research

Shandong University

Qingdao, Shandong 266237

P. R. China

Email: zhai@sdu.edu.cn