Asif Zaman

Department of Mathematics

I am an Associate Professor, Teaching Stream at the University of Toronto. Previously, I was an NSERC Postdoctoral Scholar at Stanford University working with Kannan Soundararajan. I obtained my PhD at the University of Toronto under the supervision of John Friedlander.

MAT237 EMAIL admin237@math.utoronto.ca

OTHER EMAIL asif.zaman@utoronto.ca

OFFICE PG 205D 416-978-5212

C.V.

MAILING ADDRESS Department of Mathematics
40 St. George Street, Room 6290
Toronto, ON M5S 2E4
CANADA

Research

I am interested in analytic number theory, often mixed with some probability and some algebraic number theory. Keywords usually include primes, L-functions, the Chebotarev density theorem, and random multiplicative functions. These have led to applications for class groups, binary quadratic forms, elliptic curves, and automorphic forms.

SELECTED PUBLICATIONS

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.

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.

An unconditional GL(n) large sieve.

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

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.

23. Effective Brauer-Siegel theorems for Artin L-functions

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

22. A guide to Tauberian theorems for arithmetic applications

L. B. Pierce, C. 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.
Proceedings of the American Mathematical Society. (2025), accepted.

★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. Vol. 179 (2025), No. 3, 785-819.

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).

Profiles

Teaching

I want my students to actively engage in the classroom, to collaborate in welcoming communities, to develop strong analytical skills, and to build a deeper appreciation for mathematics. If you want to learn more about teaching with class activities, then I recommend the books How Learning Works and Mathematical Mindsets as well as this AMS blog series to get started. Other online teaching resources I like are also shared below.

MAT237 MULTIVARIABLE CALCULUS WITH PROOFS

I am currently writing a textbook for this subject. It is aimed at students in quantitative sciences needing rigorous theory such as math, physics, computer science, statistics, data science, actuarial science, etc. It will hopefully be published by mid-2026, and there will be several companion teaching resources alongside it, including this (preliminary) YouTube channel.

Calculus with Fruits

youtube.com

The symbol ★ indicates I was also the coordinator for this multi-section course.

University of Toronto

2024-25	★ MAT237 Multivariable Calculus with Proofs
2023-24	★ MAT237 Multivariable Calculus with Proofs
2023 Winter	MAT198 Cryptology
2022-23	★ MAT237 Multivariable Calculus with Proofs
2021-22	★ MAT237 Multivariable Calculus with Proofs
2021 Fall	MAT198 Cryptology
2020-21	★ MAT237 Multivariable Calculus with Proofs
2020 Fall	MAT198 Cryptology
2020 Winter	MAT198 Cryptology
2019-20	★ MAT137 Calculus with Proofs

Stanford University

2019 Spring	MATH 122 Modules and Group Representations
2019 Spring	MATH 106 Functions of a Complex Variable
2018 Spring	MATH 52 Integral Calculus of Several Variables
2018 Winter	MATH 106 Functions of a Complex Variable

University of Toronto

2017 Winter	MAT135 Calculus I(A) Differential Calculus of a Single Variable
2016 Fall	MAT186 Calculus I for Engineers
2016 Summer	MAT136 Calculus I(B) Integral Calculus of a Single Variable
2015 Fall	MAT186 Calculus I for Engineers
2014 Fall	MAT186 Calculus I for Engineers
2014 Summer	MAT136 Calculus I(B) Integral Calculus of a Single Variable

Research

SELECTED PUBLICATIONS

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

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

An unconditional GL(n) large sieve.

23. Effective Brauer-Siegel theorems for Artin L-functions

22. A guide to Tauberian theorems for arithmetic applications

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

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

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

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

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

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

15. A zero density estimate for Dedekind zeta functions.

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

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

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

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

10. An unconditional GL(n) large sieve.

9. A unified and improved Chebotarev density theorem.

8. Primes represented by positive definite binary quadratic forms.

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

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

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

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

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

2. On the least prime ideal and Siegel zeros.

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

Analytic estimates for the Chebotarev Density Theorem and their applications

Profiles

MathSciNet

arXiv

Google Scholar

Teaching

MAT237 MULTIVARIABLE CALCULUS WITH PROOFS

Calculus with Fruits

University of Toronto

Stanford University

University of Toronto

Links

Quanta magazine

3Blue1Brown

LMFDB

Math3D

Desmos

Socrative

Gradescope

Ed Discussion

WeBWorK

MAT137 YouTube

Youcubed

MIT OpenCourseWare

MAA Instructional Practices

Michigan Center for IBL

Spurious correlations

Infinite Cat Project

SMBC Comics

BoardGameGeek