Research 

My research interests lie broadly in number theory, especially in modular forms and related topics. 

Periods of modular forms:

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

• 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. 

• Tianyu Ni, Hui Xue. Twisted periods of modular forms, submitted, 2025.

• Tianyu Ni, Ashley Song, Yanhui Su, Hui Xue, and Amanda Yin. Explicit generators of the space of modular forms, submitted, 2025.

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

Symmetric square L-functions:

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

• Tianyu Ni. A note on the critical values of symmetric square L-functions, to appear in Archive der Mathematik, 2025.

Shimura correspondence:

• 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.

• Abby Linscott, Tianyu Ni, Ish Shah, and Hui Xue. Shimura Lifts of nearly holomorphic modular forms, submitted, 2025.

Vector valued modular forms:

• Tianyu Ni, Hui Xue, Rankin–Cohen brackets of vector valued eisenstein series, The Ramanujan Journal, pp. 1–21, 2023. 

Hecke polynomials:

• 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. 

• Archer Clayton, Helen Dai, Tianyu Ni, Erick Ross, Hui Xue, and Jake Zummo. Non-repetition of second coefficients of Hecke polynomials, to appear in Indagationes Mathematicae, 2025.

Miscellaneous:

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

• 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.

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, Hui Xue. Twisted periods of modular forms, submitted, 2025.

11. Tianyu Ni. A note on the critical values of symmetric square L-functions, to appear in Archive der Mathematik, 2025.

12. Tianyu Ni, Ashley Song, Yanhui Su, Hui Xue, and Amanda Yin. Explicit generators of the space of modular forms, submitted, 2025.

13. Abby Linscott, Tianyu Ni, Ish Shah, and Hui Xue. Shimura Lifts of nearly holomorphic modular forms, submitted, 2025.

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