Research Papers
- Dimension Sequences for Modular Forms. Erick Ross. In preparation; it will hopefully be submitted before June 2025.
- Non-repetition of second coefficients of Hecke polynomials. Archer Clayton, Helen Dai, Tianyu Ni, Erick Ross, Hui Xue, Jake Zummo. Submitted 2024.
- Asymptotics and sign patterns of Hecke polynomial coefficients. Erick Ross, Hui Xue. Canadian Mathematical Bulletin (2025).
- On the average size of the eigenvalues of the Hecke operators. William Cason, Akash Jim, Charlie Medlock, Erick Ross, Hui Xue. Archiv der Mathematik (2025).
- Nonvanishing of second coefficients of Hecke polynomials on the newspace. William Cason, Akash Jim, Charlie Medlock, Erick Ross, Trevor Vilardi, Hui Xue. To appear in the International Journal of Number Theory.
- Signs of the second coefficients of Hecke polynomials. Erick Ross, Hui Xue. To appear in the Illinois Journal of Mathematics.
- Newspaces with Nebentypus: An Explicit Dimension Formula, Classification of Trivial Newspaces, and Character Equidistribution Property. Erick Ross. Submitted 2024.
Research Talks
- 05/2025 - When exactly will the newspaces exist? (Upcoming) 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.