PHD THESIS

Limiting distributions and zeros of Artin L-functions, Ph.D. thesis, University of British Columbia, 2000. pdf

RESEARCH ARTICLES

1. The distribution of the summatory function of the Möbius function, Proc. London Math. Soc. (3) 89 (2004) 361-389. pdf

2. The fourth moment of zeta prime rho, Duke Mathematical Journal, 125 no.2 (2004), 243-266. pdf

3. Large gaps between the zeros of the Riemann zeta function, Journal of Number Theory, 128 (2008) 509-556. pdf

4. A discrete mean value of the derivative of the Riemann zeta function, Mathematika 54 (2007), 113-155. pdf

5. Extreme values of zeta prime rho, Journal of the London Mathematical Society (2) 78 (2008), 273-289. pdf

6. The Möbius function in short intervals, Anatomy of Integers, ed. Jean-Marie De Koninck, Andrew Granville,

Florian Luca, CRM Proceedings and Lecture Notes, Volume 46, 2008, 247-258. pdf

7. The Diophantine equation A^4 + 2^d B^2 = C^p (with Michael A. Bennett and Jordan S. Ellenberg),

International Journal of Number Theory, Vol.6, No. 2 (2010), 1-27. pdf

8. A note on the gaps between consecutive zeros of the Riemann zeta function (with Hung Bui and Micah B. Milinovich),

Proceedings of the American Mathematical Society, Vol. 138, No. 12 (2010), 4167-4175. pdf

9. A note on a conjecture of Gonek (with Micah B. Milinovich), Functiones et Approximatio Commentarii Mathematici, Vol.46, No.2 (2012), 177-187. pdf

10. Explicit zero-density theorems for Dedekind zeta functions (with Habiba Kadiri), Journal of Number Theory, Vol.132 (2012), 748-775. pdf

11. Nonzero values of Dirichlet L-functions in vertical arithmetic progressions (with Greg Martin, 25 pages), International Journal of Number Theory. pdf

12. Lower bounds of moments of zeta prime rho (with Micah Milinovich, 27 pages), International Mathematics Research Notices, (2014), no. 12, 3190-3216.

13. Limiting distributions of the classical error terms of prime number theory, (with Amir Akbary and Majid Shahabi), Quarterly Journal of Mathematics, Vol. 65, No. 3 (2014), 743-780. pdf

14. Simple zeros of modular L-functions, (with Micah Milinovich), Proceedings of the London Mathematical Society, Vol. 109 (2014), No.6, 1465-1506. pdf

15. Bounds and conjectures for additive divisor sums, (with Mark Thom, 31 pages), to appear, Functiones et Approximatio Commentarii Mathematici, pdf

16. Explicit zero-density for the Riemann zeta function, (with Habiba Kadiri and Allysa Lumley), Journal of Mathematical Analysis and Applications 465 (1) (2018), 22-46.

17. The least prime ideal in the Chebotarev density theorem, (with Habiba Kadiri and Peng-Jie Wong, 15 pages), to appear, Proceedings of the American Mathematical Society.

18. Subconvexity of modular form L-functions in the t-aspect, (with Andrew Booker and Micah Milinovich, 30 pages), to appear, Advances in Mathematics.

OTHER PUBLICATIONS

19. Two appendices that appeared in Ram Murty’s article, Some remarks on the Riemann Hypothesis,

Proceedings of the Conference on L-functions and Cohomology of Arithmetic Groups, Tata Institute of

Fundamental Research, Jan. 1999, Bombay, India. pdf

20. The distribution of values of the summatory function of the Möbius function, Canadian Mathematical Society Notes, Sept. 2001, 7 pages. pdf

PREPRINTS

21. The sixth moment of the Riemann zeta function and ternary additive divisor sums, (46 pages), available on the arxiv, pdf

22. Inclusive prime number races, (with Greg Martin, 47 pages), submitted, available on the arxiv.

23. Quantitative estimates for simple zeros of L-functions, (with Andrew Booker and Micah Milinovich, 18 pages), submitted, available on the arxiv.

COLLABORATORS

Amir Akbary, University of Lethbridge.

Farzad Aryan, McGill University.

Michael Bennett, University of British Columbia.

Andrew Booker, University of Bristol.

Hung Bui, University of Manchester.

Jordan Ellenberg, University of Wisconsin.

Alia Hamieh, University of Lethbridge.

Habiba Kadiri, University of Lethbridge.

Allysa Lumley, York University.

Greg Martin, University of British Columbia.

Micah Milinovich, University of Mississippi.

Majid Shahabi, University of Calgary.

Mark Thom, University of Lethbridge.

Peng-Jie Wong, University of Lethbridge.

GRADUATE STUDENTS

Sourabhashis Das (co-supversied), Ph.D. 2018- .

Quanli Shen (co-supervised), Ph.D. 2017- .

Farzad Aryan, Ph.D (2016). Current position: postdoc at Gottingen (Germany).

Allsya Lumley (co-supervised), M.Sc. (2014). Current position: Ph.D. candidate, York University.

Majid Shahabi (co-supervised), M.Sc., 2012. Current position: Ph.D. candidate, University of Calgary.

POSTDOCS

Lee Troupe (co-supervised), 2018-2020.

Peng-Jie Wong (co-supervised), 2017-2019.

Alia Hamieh (co-supervised), 2015-2017. Current position: Assistant Professor, UNBC.

Timothy Trudgian (co-supervised), 2010-2012. Current position: ARC Early Career Research Fellow, Australian National University.

Brandon Fodden (co-supervised), 2008-2010. Current position: Instructor, Carleton University.