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Shuai Zhai

Email: zhai@sdu.edu.cn

Address: Institute for Advanced Research

Shandong University

Qingdao, Shandong 266237

Personal Homepage

Research Interests

Elliptic curves, L-functions and Modular forms.


Publications

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

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

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

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

[9] 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.

[8] 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.

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

[6] The Birch–Swinnerton-Dyer exact formula for quadratic twists of elliptic curves. Preprint, 2021.

[5] 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.

[4] Discrepancy bounds for distribution of automorphic L-functions. Lith. Math. J. 61 (2021), no. 4, 550–563. With X. Xiao.

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

[2] Integral power sums of Hecke eigenvalues over quadratic forms, Preprint, 2022. With W. Zhao.

[1] Quadratic forms, K-groups and L-values of elliptic curves, Preprint, 2023. With L. Deng and Y. Li.