Research Papers

• On Murmurations. Timothy Nelson, Erick Ross, Maya Wassercug, and Hui Xue. Submitted 08/2026, 26pp.
• Asymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspaces. Timothy Nelson, Erick Ross, Maya Wassercug, and Hui Xue. Submitted 08/2026, 30pp.
• Interlacing for zeros of the Serre derivative of Eisenstein series. Maggie Bohanek, Owen McGinty, Erick Ross, Yanhui Su, and Hui Xue. Submitted 08/2026, 51pp.
• Equidistribution of CM points and RM curves Erick Ross and Xui Xue. Submitted 05/2026. 31pp.
• Are sets with a given multiplicative structure guaranteed to have a density? Erick Ross. Acta Arithmetica, 9pp, 2026.
• Transcendence of zeros of modular forms. David Aiken, Erick Ross, Dmitriy Shvydkoy, Hui Xue. Submitted 09/2025. 15pp.
• Boundary CM points and class groups of small exponent. David Aiken, Erick Ross, Dmitriy Shvydkoy, Hui Xue. Proceedings of the AMS, 13pp, 2026.
• Zeros of even and odd period polynomials. Grace Ko, Jennifer Mackenzie, Erick Ross, Hui Xue. Journal of Mathematical Analysis and Applications, 556(1.1), 22pp, 2026.
• Proportion of Atkin-Lehner sign patterns and Hecke eigenvalue equidistribution. Erick Ross, Alexandre Van Lidth, Martha Rose Wolf, Hui Xue. Mathematical Proceedings of the Cambridge Philosophical Society, 17pp, 2026.
• Hecke eigenvalue equidistribution over the newspaces with nebentypus. Erick Ross. International Journal of Number Theory, 22(4):809-814, 2026.
• 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, 14pp, 2025.
• Non-repetition of second coefficients of Hecke polynomials. Archer Clayton, Helen Dai, Tianyu Ni, Erick Ross, Hui Xue, Jake Zummo. Indagationes Mathematicae, 22pp, 2025.
• Asymptotics and sign patterns of Hecke polynomial coefficients. Erick Ross, Hui Xue. Canadian Mathematical Bulletin, 68:914-926, 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, 124:255-263, 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, 21:1479-1512, 2025.
• Signs of the second coefficients of Hecke polynomials. Erick Ross, Hui Xue. Illinois Journal of Mathematics, 69:323-351, 2025.
• Newspaces with nebentypus: an explicit dimension formula and classification of trivial newspaces. Erick Ross. Journal of Number Theory, 278:317-352, 2026.

Research Talks

• 10/2026 (upcoming) - TBD. Number theory seminar, Kansas State University (Zoom).
• 10/2026 (upcoming) - TBD. Number theory seminar, University of Illinois Chicago.
• 10/2026 (upcoming) - Cramér α-random primes and the fundamental theorem of arithmetic. AMS (American Mathematical Society) Southeastern Sectional Meeting, Kennesaw State University.
• 10/2026 (upcoming) - Equidistribution of CM points and RM curves. AMS (American Mathematical Society) Southeastern Sectional Meeting, Kennesaw State University.
• 10/2026 (upcoming) - Dimension sequences of modular forms. AMS (American Mathematical Society) Southeastern Sectional Meeting, Kennesaw State University.
• 10/2026 (upcoming) - TBD. Number theory seminar, Louisiana State University.
• 10/2026 (upcoming) - Cramér α-random primes and the fundamental theorem of arithmetic. PANTS (PAlmetto Number Theory Series) conference, Georgia Tech.
• 08/2026 - Boundary CM points and class groups of small exponent. ANTeater (Analytic Number Theory) summer school, University of California Irvine.
• 05/2026 - Boundary CM points and class groups of small exponent. AFW (Automorphic Forms Workshop), Kansas State University.
• 05/2026 - Equidistribution of Hecke eigenvalues. AFW (Automorphic Forms Workshop), Kansas State University.
• 04/2026 - Boundary CM points and class groups of small exponent. TORA (Texas-Oklahoma Representations and Automorphic Forms) conference, University of Oklahoma.
• 04/2024 - Period polynomial zeros lie on the circle of symmetry. SERMON (SouthEastern Regional Meeting on Numbers) conference, High Point University.
• 03/2026 - Hecke eigenvalue equidistribution over the newspaces with nebentypus. AMS (American Mathematical Society) Southeastern Sectional Meeting, Georgia Southern University.
• 03/2026 - Boundary CM points and class groups of small exponent. Gainesville International Number Theory Conference, University of Florida.
• 12/2025 - Zeros of even and odd period polynomials lie on the circle of symmetry. PANTS (PAlmetto Number Theory Series) conference, Clemson University.
• 12/2025 - Cramér α-random primes and the fundamental theorem of arithmetic. GSS (Graduate Student Seminar), Clemson University.
• 11/2025 - Dimension sequences of modular forms. BARD (Bayou Arithmetic Research Day), Louisiana State University (Zoom).
• 11/2025 - Cramér α-random primes and the fundamental theorem of arithmetic. MSS (Mathematical Sciences Symposium), Bob Jones University.
• 10/2025 - 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.

Expository Papers

• Three Density-One Formulations of Convergence. Erick Ross, Alexandre Van Lidth, Martha Rose Wolf, Hui Xue. Submitted 09/2025.

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