Profile
Tianyu Ni
Mathematical and Statistical Sciences
Graduate Grader Assistant
Jordan Hall G15 [Office]
Educational Background
MS, Arts and Mathematics, Brandeis University, 2021
MS, Pure Mathematics, Sichuan University, 2019
BA, Mathematics, Northwest University, 2016
Research Interests
My general interest is in Number Theory. I am currently working in Modular Forms, including
periods of modular forms, symmetric square L-functions, explicit Shimura correspondence, vector-valued modular forms, and Hecke polynomials.
Courses Taught
Business Calculus I, Business Calculus II.
Selected Publications
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.
Selected Talks
1. September 24, 2022. Linear independence of odd periods of modular forms. Palmetto Number Theory Series 34, Charlotte, NC.
2. December 11, 2022. Rankin-Cohen brackets of vector valued forms, Palmetto Number Theory Series 35, Columbia, SC.
3. December 9, 2023. Eichler-Shimura relations for derivative periods of modular forms, Palmetto Number Theory XXXVII, Athens, GA.
4. April 28, 2024. Linear independence of periods for the symmetric square L-functions, Southeastern Regional Meeting on Numbers, Spartanburg, SC.
5. May 21, 2024. Explicit linear relations between special values of derivatives of L-fucntions. 36th Automorphic Forms Workshop, Stillwater, OK.
6. September 21, 2024. Shimura lift and non-vanishing of twisted central L-values, Palmetto
Number Theory Series 38, Winston-Salem, NC.
7. December 7, 2024. Shimura lift of Rankin-Cohen brackets of Eisenstein series and theta function, Palmetto Number Theory Series 39, Columbia, SC.
8. April 12, 2025. Twisted periods of modular forms, Southeastern Regional Meeting on Numbers, Savannah, GA.
9. December 6, 2025. KernelfunctionsofthesymmetricsquareL-functionsofmodularforms, Palmetto Number Theory Series 40, Clemson, SC.
Honors and Awards
Sobczyk Fellowship, ($ 5000), Clemson University, School of Mathematical and Statistical Sciences 2021
Outstanding Graduate in Research Award School of Mathematical and Statistical Sciences, Clemson University 2025
AMS Sectional Travel Grant for March 2026 meeting, ($ 400), Georgia Southern University-Armstrong Campus, Savannah, GA
Expected Graduation
2026 December
