Research

Selected Publications:  Publications and Preprints

1. (with Yifan Yang)   Jacquet-Langlands correspondence for non-Eichler orders. arXiv: 2509.02985

2. (with Michael Allen, Brian Grove, and Ling Long)   The Explicit Hypergeometric-Modularity Method II. arXiv: 2411.15116

3. (with Jerome William Hoffman, Wen-Ching Winnie Li, and Ling Long) Traces of Hecke Operators Via Hypergeometric Character Sums. arXiv: 2408.02918 (submitted)

4. (with Jerome William Hoffman)     QM Abelian Varieties, Hypergeometric Character Sums, and Modular Forms. (Survey, to appear) arXiv: 2408.06562

5. (with Jerome William Hoffman)    Transformations of Hypergeometric Motives.  arXiv: 2003.05031 

6. (with Angelica Babei, Manami Roy, Holly Swisher, Bella Tobin) Supercongruences arising from Ramanujan-Sato Series. Results in Mathematics 80 (6), 184, 2025. 

7. (with Michael Allen, Brian Grove, and Ling Long)   The Explicit Hypergeometric-Modularity Method I.  Advances in Mathematics, Vol. 478, 2025. 

8. (with Angelica Babei, Lea Beneish, Manami Roy, Holly Swisher, Bella Tobin) Generalized Ramanujan-Sato Series arising from Modular Forms.  Research Directions in Number Theory: Women in Numbers V, 87-131, 2024. 

9. (with Wen-Ching Winnie Li, and Ling Long)  A Whipple $7F6$ formula revisited.   La Matematica 1-51, 2022

10. (with Jenny G. Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher)  Hypergeometric Functions over Finite Fields.   Mem. Amer. Math. Soc. 280 (2022), no. 1382.. 

11. (with Ling Long, Noriko Yui and Wadim Zudilin) Supercongruences for Rigid Hypergeometric Calab-Yau Threefolds.  Advances in Mathematics, Vol. 393, 2021.    (numerical computations in SageMath and Database of Hecke eigenforms)

12. (with Wen-Ching Winnie Li, and Ling Long) Computing Special L-values of Certain Modular Forms with Complex Multiplication. arXiv: 1803.06072​ SIGMA 14 (2018), 090, 32 pages

13. (with Yifan Yang) Evaluation of Certain Hypergeometric Functions over Finite Fields. eprint arXiv: 1711.05842, SIGMA 14 (2018), 050, 18 pages.

14. (with Sharon Frechette and Holly Swisher) A Cubic Transformation Formula for Appell-Lauricella Hypergeometric Functions over Finite Fields. arXiv: 1701.04526  Research in Number Theory (2018) 4:27

15. (with Alyson Deines, Jenny G. Fuselier, Ling Long,  and Holly Swisher) Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions. Directions in Number Theory, Proceedings for Women in Numbers 3, AWM series, 125-159. (2016)

16. (with Alyson Deines, Jenny G. Fuselier, Ling Long,  and Holly Swisher) Generalized Legendre Curves and Quaternionic Multiplicati. J. Number Theory, 161 (2016), 175-203

Grants:
I gratefully acknowledge  the NSF, the SLMath, the AWM, and the NSA and the NTF  for funding my research/conference endeavors. 

1. NSF research grant (DMS #2302531, 2023--2026)

2. NSF Conference Grant (2341365, $35,000): Southern Regional Number Theory Conference (2024--2026)  PI: Gene Kopp

3. SLMath 2023 Summer Research in Mathematics (6/12-6/23/2023). Group Members: Angelica Babei, Manami Roy, Holly Swisher, and Bella Tobin.

4. NSF Conference Grant (1951773, $29,931): Southern Regional Number Theory Conference (2020--2022) Co-PI: Ling Long

5. NSA Conference Grant (H98230-21-1-0005, $11,220): Southern Regional Number Theory Conference (optional year: 2022) Co-PI: Ling Long

6. AWM-NSF Mathematics Mentoring Travel Grants (4/1/2017-6/30/2018)

Mentor: Wen-Ching Winnie Li