Asif Zaman

My research is focused on analytic and probabilistic number theory with applications to algebraic structures and arithmetic statistics. I have investigated problems concerning the distribution of prime numbers, zeros of L-functions, the Chebotarev density theorem, random multiplicative functions, and binary quadratic forms. These have led to applications involving elliptic curves, automorphic forms, torsion in class groups, and mass equidistribution on the modular surface.

List of papers

Preprints on arXiv.org may differ slightly from the published journal articles. Authorship is always listed in alphabetical order by last name. The symbol ★ indicates articles written as part of undergraduate research programs.

22. A guide to Tauberian theorems for arithmetic applications

Lillian B. Pierce, Caroline L. Turnage-Butterbaugh, A. Zaman.
submitted (2025).

21. Improving the trivial bound for ell-torsion in class groups.

R. J. Lemke Oliver, A. Zaman.
submitted (2025).

20. Explicit Deuring-Heilbronn phenomenon for Dirichlet L-functions.

K. Benli, S. Goel, H. Twiss, A. Zaman.
submitted (2024).

★19. Moments of random multiplicative functions over function fields.

M. C. E. Hofmann, A. Hoganson, S. Menon, W. Verreault, A. Zaman.
Mathematical Proceedings of the Cambridge Philosophical Society. (2025), accepted.

18. An explicit version of Bombieri's log-free density estimate and Sarkozy's theorem for shifted primes.

J. Thorner, A. Zaman.
Forum Mathematicum. Vol. 36 (2024), No. 4, 1059-1080.

17. Refinements to the prime number theorem for arithmetic progressions.

J. Thorner, A. Zaman.
Mathematische Zeitschrift. Vol. 306 (2024), No. 54.

16. An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin L-functions.

R. J. Lemke Oliver, J. Thorner, A. Zaman.
Inventiones Mathematicae. Vol. 235 (2024), 893-971.

15. A zero density estimate for Dedekind zeta functions.

J. Thorner, A. Zaman.
International Mathematics Research Notices., Vol. 2023 (2023), No. 8, 6739-6761.

★14. A conjectural asymptotic formula for multiplicative chaos in number theory.

D. Aggarwal, U. Subedi, W. Verreault, A. Zaman, C. Zheng.
Research in Number Theory. Vol. 8 (2022), No. 35.

★13. Sums of random multiplicative functions over function fields with few irreducible factors.

D. Aggarwal, U. Subedi, W. Verreault, A. Zaman, C. Zheng.
Mathematical Proceedings of the Cambridge Philosophical Society., Vol. 173 (2022), No. 3, 715-726.

12. A model problem for multiplicative chaos in number theory.

K. Soundararajan, A. Zaman.
L'Enseignement Mathématique. Vol. 68 (2022), No. 3, 307-340.

11. Zeros of Rankin-Selberg L-functions at the edge of the critical strip.

F. Brumley, J. Thorner, A. Zaman. With an appendix by C. J. Bushnell and G. Henniart.
Journal of the European Mathematical Society. Vol. 24 (2022), No. 5, 1471-1541.

10. An unconditional GL(n) large sieve.

J. Thorner, A. Zaman.
Advances in Mathematics. Vol. 378 (2021), 107529.

9. A unified and improved Chebotarev density theorem.

J. Thorner, A. Zaman.
Algebra & Number Theory. Vol. 13 (2019), No. 5, 1039-1068.

8. Primes represented by positive definite binary quadratic forms.

A. Zaman.
The Quarterly Journal of Mathematics. Vol. 69 (2018), No. 4, 1353-1386.

7. The density of numbers represented by diagonal forms of large degree.

B. Hanson, A. Zaman.
Mathematika. Vol. 64 (2018), No. 2, 542-550.

6. The least unramified prime which does not split completely.

A. Zaman.
Forum Mathematicum. Vol. 30 (2017), No. 3, 651-661.

5. A Chebotarev variant of the Brun-Titchmarsh theorem and bounds for the Lang-Trotter conjectures.

J. Thorner, A. Zaman.
International Mathematics Research Notices. Vol. 2018 (2018), No. 16, 4991-5027.

4. An explicit bound for the least prime ideal in the Chebotarev density theorem.

J. Thorner, A. Zaman.
Algebra & Number Theory. Vol. 11 (2017), No. 5, 1135-1197.

3. Bounding the least prime ideal in the Chebotarev Density Theorem.

A. Zaman.
Functiones et Approximatio Commentari Mathematici. Vol. 57 (2017), No. 1, 115-142.

2. On the least prime ideal and Siegel zeros.

A. Zaman.
International Journal of Number Theory. Vol. 12 (2016), No. 8, 2201-2229.

1. Explicit estimates for the zeros of Hecke L-functions.

A. Zaman.
Journal of Number Theory. Vol. 162 (2016), 312-375.

Analytic estimates for the Chebotarev Density Theorem and their applications

A. Zaman.
PhD thesis. University of Toronto (2017).

I want my students to actively and equitably engage in the classroom, to collaborate in welcoming communities, to develop strong analytical skills, and to build a deeper appreciation for mathematics. For some ideas on active learning for all experience levels, I recommend the books Mathematical Mindsets and How Learning Works. I also like this AMS blog series. Other online teaching resources I like are also shared below.

List of courses