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.
Papers are listed roughly in reverse chronological order. Preprints on arXiv.org may differ slightly from the published journal articles.
16. Refinements to the prime number theorem for arithmetic progressions.J. Thorner, A. Zaman. (2021), submitted.
14. A model problem for multiplicative chaos in number theory.K. Soundararajan, A. Zaman. (2021), submitted.
9. A unified and improved Chebotarev density theorem.J. Thorner, A. Zaman. Algebra & Number Theory. Vol. 13 (2019), No. 5, 1039-1068.
7. The density of numbers represented by diagonal forms of large degree.B. Hanson, A. Zaman. Mathematika. Vol. 64 (2018), No. 2, 542-550.
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.
I want my students to actively engage in the classroom, to develop strong analytical skills for their future studies and careers, and to build a deeper appreciation for mathematics. I recommend the book How Learning Works and this AMS blog series for some ideas on active learning for all experience levels. Other online teaching resources I like to use are also shared below.
University of Toronto
|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|
|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|