Asif Zaman

My research is focused on analytic 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, and binary quadratic forms. These have led to interesting applications involving elliptic curves, modular forms, torsion in class groups, and mass equidistribution on the modular surface. Recently, I have also been studying random multiplicative functions.

List of papers

Papers are listed roughly in reverse chronological order. Preprints on arXiv.org may differ slightly from the published journal articles.

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

J. Thorner, A. Zaman. Forum Math. (2024), published online.

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

J. Thorner, A. Zaman. Math. Z. 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. Invent. Math. Vol. 235 (2024), 893-971.

15. A zero density estimate for Dedekind zeta functions.

J. Thorner, A. Zaman. Int. Math. Res. Not., 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. Res. 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. Math. Proc. Camb. Phil. Soc., Vol. 173 (2022), No. 3, 715-726.

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

K. Soundararajan, A. Zaman. Enseign. Math. 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. J. Eur. Math. Soc. Vol. 24 (2022), No. 5, 1471-1541.

10. An unconditional GL(n) large sieve.

J. Thorner, A. Zaman. Adv. Math. 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. Q. J. Math. 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 Math. 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. Int. Math. Res. Not. 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. Funct. Approx. Comment. Math. Vol. 57 (2017), No. 1, 115-142.

2. On the least prime ideal and Siegel zeros.

A. Zaman. Int. J. Number Theory. Vol. 12 (2016), No. 8, 2201-2229.

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

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

Analytic estimates for the Chebotarev Density Theorem and their applications

A. Zaman. PhD thesis (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