.: Summer Research Experiences program


The Summer Research Experiences program is aimed at undergraduate students who are interested in obtaining experience in number theory research topics.


Summer 2024 program


Matching densities for automorphic L-functions, run by N. Walji.

Graduate mentor: Kin Ming Tsang.


Natural language processing and machine learning, run by L. Daniels.



Summer 2023 program

On the distribution of traces of Frobenius for elliptic curves, run by N. Walji.

Graduate mentor: Kin Ming Tsang.


Summer 2022 program

On the distribution of coefficients of GL(2) automorphic L-functions, run by N. Walji.

Heuristics for a variant of the Lang-Trotter conjecture for elliptic curves, run by N. Walji.

Local to global principle for expected values over function fields, run by S. Schraven. PDF summary
arXiv link to paper: https://arxiv.org/abs/2212.00895


Summer 2021 program

Congruence class bias and the Lang-Trotter conjecture

For various families of elliptic curves over the integers, we demonstrate the existence of congruence class bias with respect to the Lang-Trotter conjecture. We also investigate such questions computationally for individual elliptic curves. Lastly, we show that the heuristics for the distribution of traces of Frobenius for elliptic curves are consistent with our observations of congruence class bias on average.

Paper: S. Jarov, A. Khadra, N. Walji, Congruence class bias and the Lang-Trotter conjecture for families of elliptic curves. To appear in Involve.



.: Earlier Student Projects

Students have worked with me in areas related to:
• Elliptic curves
• L-functions
• Group theory

Past project topics have included:
• The Lang-Trotter conjecture
• Refinements of strong multiplicity one for automorphic L-functions
• Occurrence of Hecke eigenvalues for pairs of Maass forms.