Research

Elliptic Curves, Birch and Swinnerton-Dyer Conjecture.

Papers

• Elliptic curves with complex multiplication and the 2-part of the Birch and Swinnerton-Dyer conjecture. Preprint. With J. Coates.
• Discrepancy bounds for distribution of automorphic L-functions. Lith. Math. J. 61 (2021), no. 4, 550--563. With X. Xiao.
• 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. Preprint. 
• Non-vanishing of L-values of elliptic curves and the conjectures of Birch and Swinnerton-Dyer and of Goldfeld. Preprint. 
• 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 GL_m. Front. Math. China 7 (2012), no. 5, 883--894. With Y. Qu. 

Address

Department of Pure Mathematics and Mathematical Statistics

Centre for Mathematical Sciences

University of Cambridge

Cambridge CB3 0WB

United Kingdom

Email: shuaizhai@gmail.com