Asif Zaman

Mathematics, University of Toronto

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.

I am interested in number theory. I apply analytic and probabilistic techniques to study L-functions, primes, random multiplicative functions, and other arithmetic objects. These interests have led to problems involving class groups, binary quadratic forms, elliptic curves, automorphic forms, and arithmetic statistics.

MAT237 Email

admin237@math.utoronto.ca

Other Email

asif.zaman@utoronto.ca

Office

PG 205D · 416-978-5212

C.V.

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Mailing Address

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

Research

MathSciNet

Google Scholar

arXiv

GitHub

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.

arXiv DOI code

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.

arXiv DOI

An unconditional GL(n) large sieve

J. Thorner, A. Zaman

Advances in Mathematics. Vol. 378 (2021), 107529.

arXiv DOI

Research Supervision

I am currently accepting PhD and MSc students. Prospective students should apply through the University of Toronto graduate admissions process.

I also often supervise undergraduate summer research through either the Department of Mathematics Summer Research Awards or the Fields Institute Undergraduate Summer Research Program. Please check both websites to see if I am currently proposing a project.

If you are interested in any of the above, please feel free to contact me once you have submitted your application to the corresponding program.

All Preprints and Publications

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.

★26

Numerical computations concerning Landau-Siegel zeros

R. F. Lu, A. Zaman, H. Zhao

Mathematics of Computation (2026), to appear.

arXiv code

The least prime with a given cycle type

P. J. Cho, R. J. Lemke Oliver, A. Zaman

(2025), submitted.

arXiv code

★24

Central limit theorems for random multiplicative functions over function fields

D. Hoban, J. I. Shah, N.-C. Ismail, W. Verreault, A. Zaman

Research in the Mathematical Sciences. Vol. 13 (2026), No. 58.

arXiv DOI

Effective Brauer-Siegel theorems for Artin L-functions

P. J. Cho, R. J. Lemke Oliver, A. Zaman

(2025), submitted.

arXiv

A guide to Tauberian theorems for arithmetic applications

L. B. Pierce, C. L. Turnage-Butterbaugh, A. Zaman

Essential Number Theory. (2026), to appear.

arXiv

Improving the trivial bound for ℓ-torsion in class groups

R. J. Lemke Oliver, A. Zaman

(2025), submitted.

arXiv

Explicit Deuring-Heilbronn phenomenon for Dirichlet L-functions

K. Benli, S. Goel, H. Twiss, A. Zaman

Proceedings of the American Mathematical Society. Vol. 154 (2026), 509-525.

arXiv DOI

★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.

arXiv DOI

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.

arXiv DOI

Refinements to the prime number theorem for arithmetic progressions

J. Thorner, A. Zaman

Mathematische Zeitschrift. Vol. 306 (2024), No. 54.

arXiv DOI

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.

arXiv DOI

A zero density estimate for Dedekind zeta functions

J. Thorner, A. Zaman

International Mathematics Research Notices. Vol. 2023 (2023), No. 8, 6739-6761.

arXiv DOI

★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.

arXiv DOI code

★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.

arXiv DOI

A model problem for multiplicative chaos in number theory

K. Soundararajan, A. Zaman

L'Enseignement Mathematique. Vol. 68 (2022), No. 3, 307-340.

arXiv DOI

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.

arXiv DOI

An unconditional GL(n) large sieve

J. Thorner, A. Zaman

Advances in Mathematics. Vol. 378 (2021), 107529.

arXiv DOI

A unified and improved Chebotarev density theorem

J. Thorner, A. Zaman

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

arXiv DOI

Primes represented by positive definite binary quadratic forms

A. Zaman

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

arXiv DOI

The density of numbers represented by diagonal forms of large degree

B. Hanson, A. Zaman

Mathematika. Vol. 64 (2018), No. 2, 542-550.

arXiv DOI

The least unramified prime which does not split completely

A. Zaman

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

arXiv DOI

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.

arXiv DOI

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.

arXiv DOI

Bounding the least prime ideal in the Chebotarev Density Theorem

A. Zaman

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

arXiv DOI

On the least prime ideal and Siegel zeros

A. Zaman

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

arXiv DOI

Explicit estimates for the zeros of Hecke L-functions

A. Zaman

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

arXiv DOI

Analytic estimates for the Chebotarev Density Theorem and their applications

A. Zaman

PhD thesis. University of Toronto (2017).

PDF Handle

Teaching

My teaching focuses on creating opportunities for students to actively engage in the classroom, to collaborate with one another, and to develop confidence in their thinking. I am particularly interested in how students learn to:

read, write, and speak mathematics with increasing independence
connect multiple representations of mathematical ideas
build learning communities that support productive struggle

These interests inform my approach to course design and have motivated the development of a textbook, interactive visualizations, tactile models, classroom activities, and educational videos.

A variety of resources have influenced my approach to teaching, including How Learning Works, Mathematical Mindsets, and an AMS blog series on active learning.

Advanced Calculus in Several Variables

I am currently writing a textbook for this subject based on my experience teaching MAT237 Multivariable Calculus with Proofs for many years. It is designed for students in quantitative sciences needing rigorous theory such as math, physics, computer science, statistics, data science, actuarial science, and more. It will hopefully be published by the end of 2026. There will be several companion teaching resources alongside it, including this preliminary YouTube channel Calculus with Fruits.

Latest from Calculus with Fruits

7.6 Sets with Zero Jordan Measure

9.4 Fubini's Theorem in 3D

11.1 Curves

Visit the channel

Courses Taught

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

University of Toronto

2024-25	★MAT237 Multivariable Calculus with Proofs
2024 Fall	MAT496 Independent Reading in Math: Computation with L-functions
2023-24	★MAT237 Multivariable Calculus with Proofs
2023 Winter	MAT198 Cryptology
2023 Summer	MAT1900 Readings in Pure Math: Sieve Theory and Binary Quadratic Forms
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

Asif Zaman

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

Research Supervision

All Preprints and Publications

Numerical computations concerning Landau-Siegel zeros

The least prime with a given cycle type

Central limit theorems for random multiplicative functions over function fields

Effective Brauer-Siegel theorems for Artin L-functions

A guide to Tauberian theorems for arithmetic applications

Improving the trivial bound for ℓ-torsion in class groups

Explicit Deuring-Heilbronn phenomenon for Dirichlet L-functions

Moments of random multiplicative functions over function fields

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

Refinements to the prime number theorem for arithmetic progressions

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

A zero density estimate for Dedekind zeta functions

A conjectural asymptotic formula for multiplicative chaos in number theory

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

A model problem for multiplicative chaos in number theory

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

An unconditional GL(n) large sieve

A unified and improved Chebotarev density theorem

Primes represented by positive definite binary quadratic forms

The density of numbers represented by diagonal forms of large degree

The least unramified prime which does not split completely

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

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

Bounding the least prime ideal in the Chebotarev Density Theorem

On the least prime ideal and Siegel zeros

Explicit estimates for the zeros of Hecke L-functions

Analytic estimates for the Chebotarev Density Theorem and their applications

Teaching

Advanced Calculus in Several Variables

Courses Taught

University of Toronto

Stanford University

University of Toronto

Links

Teaching & math resources

Just for fun