Ng, Nathan
Faculty
Mathematics ＆ Computer Science
- Phone
- (403) 329-5118
- nathan.ng@uleth.ca
Biography
Bachelor of Science, UBC, 1994
Master of Science, University of Toronto, 1995
PhD., UBC, 2000
Canadian Mathematical Society Doctoral Prize 2001
Postdoctoral Associate, University of Georgia, 2001-2002
Member, Institute for Advanced Study, Princeton, NJ, Spring 2002
Postdoc, Universite de Montreal, 2002-2004
Assistant Professor (tenure-track), University of Ottawa, 2004-2008
Visiting assistant professor, University of Michigan, 2004-2005
Assistant professor, Lethbridge, 2008-2010
Associate professor, Lethbridge, 2010-2019
Professor, Lethbridge, since 2019.
PIMS Site Director, Lethbridge, since 2019.
Master of Science, University of Toronto, 1995
PhD., UBC, 2000
Canadian Mathematical Society Doctoral Prize 2001
Postdoctoral Associate, University of Georgia, 2001-2002
Member, Institute for Advanced Study, Princeton, NJ, Spring 2002
Postdoc, Universite de Montreal, 2002-2004
Assistant Professor (tenure-track), University of Ottawa, 2004-2008
Visiting assistant professor, University of Michigan, 2004-2005
Assistant professor, Lethbridge, 2008-2010
Associate professor, Lethbridge, 2010-2019
Professor, Lethbridge, since 2019.
PIMS Site Director, Lethbridge, since 2019.
Publications
The distribution of the summatory function of the Mobius function, Proc. London Math. Soc. (3) 89 (2004) 361-389.
The fourth moment of zeta prime rho, Duke Mathematical Journal, 125 no.2 (2004), 243-266.
The Möbius function in short intervals, Anatomy of Integers, CRM Proceedings and Lecture Notes, Volume 46, 2008, 247-258.
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.
Lower bounds of moments of zeta prime rho (with Micah Milinovich), International Mathematics Research Notices, (2014), no. 12, 3190-3216.
Simple zeros of modular L-functions, (with Micah Milinovich), Proc. London Math. Soc., Vol. 109 (2014), No.6, 1465-1506.
The least prime ideal in Chebotarev's density theorem (with Habiba Kadiri and Peng-Jie Wong), Proceedings of the AMS, 147 (2019), 2289-2303.
Subconvexity for modular form L-functions in the t aspect (with Andrew Booker and Micah Milinovich), Advances in Mathematics 341 (2019), 299-335
Inclusive prime number races (with Greg Martin), Transactions of the AMS, 373 (2020), 3561-3607.
The sixth moment of the Riemann zeta function and ternary additive divisor sums, (56 pages), available on the arXiv.
The fourth moment of zeta prime rho, Duke Mathematical Journal, 125 no.2 (2004), 243-266.
The Möbius function in short intervals, Anatomy of Integers, CRM Proceedings and Lecture Notes, Volume 46, 2008, 247-258.
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.
Lower bounds of moments of zeta prime rho (with Micah Milinovich), International Mathematics Research Notices, (2014), no. 12, 3190-3216.
Simple zeros of modular L-functions, (with Micah Milinovich), Proc. London Math. Soc., Vol. 109 (2014), No.6, 1465-1506.
The least prime ideal in Chebotarev's density theorem (with Habiba Kadiri and Peng-Jie Wong), Proceedings of the AMS, 147 (2019), 2289-2303.
Subconvexity for modular form L-functions in the t aspect (with Andrew Booker and Micah Milinovich), Advances in Mathematics 341 (2019), 299-335
Inclusive prime number races (with Greg Martin), Transactions of the AMS, 373 (2020), 3561-3607.
The sixth moment of the Riemann zeta function and ternary additive divisor sums, (56 pages), available on the arXiv.
Research Interests
My area of research is analytic number theory. My main area of interest is the theory of the Riemann zeta function and L-functions. However, I am also interested in a variety of problems in analytic number theory. Some of the recent topics I have worked on are: moments of the Riemann zeta function, simple zeros of L-functions, mean values of L-functions, non-vanishing of L-functions, the least prime in Chebotarev's density theorem, sums over the zeros of the zeta function, gaps between zeros of the zeta function, mean value estimates for Dirichlet polynomials, convolution sums of arithmetic functions, and various questions concerning prime number races and distribution functions of number theoretic functions.