Research Papers
- Transcendence of zeros of modular forms. David Aiken, Erick Ross, Dmitriy Shvydkoy, Hui Xue. Submitted 09/2025.
- Boundary CM points and class groups of small exponent. David Aiken, Erick Ross, Dmitriy Shvydkoy, Hui Xue. Submitted 09/2025.
- Zeros of Even and Odd Period Polynomials. Grace Ko, Jennifer Mackenzie, Erick Ross, Hui Xue. Submitted 08/2025.
- Proportion of Atkin-Lehner sign patterns and Hecke Eigenvalue Equidistribution. Erick Ross, Alexandre Van Lidth, Martha Rose Wolf, Hui Xue. Under revision with Mathematical Proceedings of the Cambridge Philosophical Society.
- Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus. Erick Ross. Submitted 06/2025.
- Cramér α-random primes and the Fundamental Theorem of Arithmetic. Erick Ross. Submitted 05/2025.
- Dimension Sequences of Modular Forms. Erick Ross. Research in Number Theory (2025), 14pp.
- Non-repetition of second coefficients of Hecke polynomials. Archer Clayton, Helen Dai, Tianyu Ni, Erick Ross, Hui Xue, Jake Zummo. Indagationes Mathematicae (2025), 22pp.
- Asymptotics and sign patterns of Hecke polynomial coefficients. Erick Ross, Hui Xue. Canadian Mathematical Bulletin, 68 (2025) 914-926.
- On the average size of the eigenvalues of the Hecke operators. William Cason, Akash Jim, Charlie Medlock, Erick Ross, Hui Xue. Archiv der Mathematik, 124 (2025) 255-263.
- Nonvanishing of second coefficients of Hecke polynomials on the newspace. William Cason, Akash Jim, Charlie Medlock, Erick Ross, Trevor Vilardi, Hui Xue. International Journal of Number Theory, 21 (2025) 1479-1512.
- Signs of the second coefficients of Hecke polynomials. Erick Ross, Hui Xue. Illinois Journal of Mathematics, 69 (2025) 323-351.
- Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces. Erick Ross. Journal of Number Theory, 278 (2026) 317-352.
Research Talks
- 11/2025 (upcoming) Dimension Sequences of Modular Forms. BARD (Bayou Arithmetic Research Day), Louisiana State University.
- 11/2025 (upcoming) - Cramér α-random primes and the Fundamental Theorem of Arithmetic. Bob Jones University Mathematical Sciences Symposium, Bob Jones University.
- 10/2025 (upcoming) - What is the asymptotic behavior of the Hecke polynomial coefficients? Maine-Quebec Number Theory Conference, University of Maine.
- 09/2025 - Asymptotics and Sign Patterns for the Hecke Polynomial Coefficients. GSS (Graduate Student Seminar), Clemson University.
- 05/2025 - When exactly will the newspaces exist? AFW (Automorphic Forms Workshop), University of North Texas.
- 03/2025 - When precisely will the newspaces of modular forms exist? AMS (American Mathematical Society) Southeastern Sectional Meeting, Clemson University.
- 03/2025 - How large can we expect the newspaces to be? GSS (Graduate Student Seminar), Clemson University.
- 12/2024 - How large are the eigenvalues of the Hecke operators? PANTS (PAlmetto Number Theory Series) conference, University of South Carolina.
- 09/2024 - Nonvanishing of second coefficients of Hecke polynomials on the newspace. PANTS (PAlmetto Number Theory Series) conference, Wake Forest University.
- 09/2024 - How large are the Hecke eigenvalues and corresponding Fourier coefficients? GSS (Graduate Student Seminar), Clemson University.
- 05/2024 - Nonvanishing of the Second Coefficient of General Hecke Polynomials. AFW (Automorphic Forms Workshop), Oklahoma State University.
- 04/2024 - Eigenbasis Decomposition of Hecke Eigenform Products via the Rankin-Selberg Method. SERMON (SouthEastern Regional Meeting on Numbers) conference, Wofford College.
- 02/2024 - From Tori to Elliptic Curves. DECAL (Data sECurity and mAchine Learning) Research Workshop, Clemson University.