Research Papers
- Cramer $\alpha$-random primes and the Fundamental Theorem of Arithmetic. Erick Ross. Submitted 05/2025.
- Dimension Sequences of Modular Forms. Erick Ross. Submitted 04/2025.
- Non-repetition of second coefficients of Hecke polynomials. Archer Clayton, Helen Dai, Tianyu Ni, Erick Ross, Hui Xue, Jake Zummo. To appear in Indagationes Mathematicae.
- 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. International Journal of Number Theory (2025).
- Signs of the second coefficients of Hecke polynomials. Erick Ross, Hui Xue. To appear in Illinois Journal of Mathematics.
- Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces. Erick Ross. To appear in Journal of Number Theory.
Research Talks
- 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.