Research 

I work in Number Theory. My current research topics lie in elliptic modular forms, including periods of modular forms, symmetric square L-functions, explicit Shimura correspondence, vector-valued modular forms, and Hecke polynomials.

Publications and preprints

1. Tianyu Ni . On the gap between prime ideals. AIMS Math., 4(1):79–85, 2019.

2. Austin Lei, Tianyu Ni, and Hui Xue. Linear independence of even periods of modular forms. J. Number Theory, vol. 248, pp. 120–139, 2023.

3. Austin Lei, Tianyu Ni, and Hui Xue. Linear independence of odd periods of modular forms. Res. Number Theory, 9(2):Paper No. 33, 20, 2023.

4. Tianyu Ni and Hui Xue. Rankin-Cohen brackets of vector valued Eisenstein series. Ramanujan J., 62(4):1145–1165, 2023.

5. Archer Clayton, Helen Dai, Tianyu Ni, Hui Xue, and Jake Zummo. Nonvanishing of second coefficients of Hecke polynomials. J. Number Theory, 262:186–221, 2024.

6. June Kayath, Connor Lane, Ben Neifeld, Tianyu Ni, and Hui Xue. AGM aquariums and elliptic curves over arbitrary finite fields. Res. Number Theory, 11(2):Paper No. 48, 2025.

7. Tianyu Ni, Hui Xue. Linear independence of periods for the symmetric square L-functions. Ann. Math. Qué., 49(2):445–462, 2025.

8. June Kayath, Connor Lane, Ben Neifeld, Tianyu Ni, and Hui Xue. Subspaces spanned by eigenforms with nonvanishing twisted central L-values, to appear in Canadian Journal of Mathematics, 2025.

9. Archer Clayton, Helen Dai, Tianyu Ni, Erick Ross, Hui Xue, and Jake Zummo. Non-repetition of second coefficients of Hecke polynomials. Indag. Math. (N.S.), 37(4):1117–1135, 2026.

10. Tianyu Ni and Hui Xue. Twisted periods of modular forms. Nagoya Math. J., 261:e18, 2026.

11. Tianyu Ni . A note on the critical values of symmetric square L-functions. Arch. Math. (Basel), 126(1):53–60, 2026.

12. Tianyu Ni, Ashley Song, Yanhui Su, Hui Xue, and Amanda Yin. Explicit generators of the space of modular forms. Ramanujan J., 70(3):47, 2026.

13. Abby Linscott, Tianyu Ni, Ish Shah, and Hui Xue. Shimura lifts of nearly holomorphic modular forms. Internat. J. Math., 37(7):Paper No. 2650032, 22, 2026.

14. Tianyu Ni and Hui Xue. Periods and symmetric square periods of modular forms. Manuscripta Math., 177(4):Paper No. 51, 2026.

15. Tianyu Ni . Representation of Ramanujan’s tau function by twisted divisor functions. Int. J. Number Theory, 22(7):1525–1539, 2026.

16. Tianyu Ni, Milo Stammers, Hui Xue, and Sarah Yan. Linear independence of Poincaré series, submitted, 2026.

17. Tianyu Ni, Milo Stammers, Hui Xue, and Sarah Yan. Traces of Rankin-Cohen brackets of Eisenstein series, submitted, 2026.

18. Tianyu Ni . Rational spanning sets of level-one cusp forms from Eisenstein series at prime levels, submitted, 2026.

19. Tianyu Ni, Milo Stammers, Hui Xue, and Sarah Yan. Linear combinations of cuspidal projections of products of Eisenstein series, submitted, 2026.