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.

Publication List

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

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

3. Austin Lei, Tianyu Ni, Hui Xue, Linear independence of odd periods of modular forms,” Res. Number Theory, vol. 9, no. 2, Paper No. 33, 2023. 

4. Tianyu Ni, Hui Xue, Rankin–Cohen brackets of vector valued eisenstein series, The Ramanujan Journal, pp. 1–21, 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. Tianyu Ni, Hui Xue, Linear independence of periods for the symmetric square L-functions. Ann. Math. Qué., 49(2):445-462, 2025.

7. June Kayath, Connor Lane, Ben Neifeld, Tianyu Ni, and Hui Xue. Subspaces spanned by eigenforms with nonvanishing twisted central L-values, submitted, 2024.

8. Archer Clayton, Helen Dai, Tianyu Ni, Erick Ross, Hui Xue, and Jake Zummo. Non-repetition of second coefficients of Hecke polynomials, submitted, 2024.

9. 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.

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, Hui Xue. Periods and symmetric periods of modular forms, submitted, 2025.

15. Tianyu Ni. Representation of Ramanujan’s tau function by twisted divisor functions, submitted, 2025.