Nathan Ng | PIMS - Pacific Institute for the Mathematical Sciences

PIMS Site Director & Professor of Mathematics, University of Lethbridge

Prof. Nathan Ng is the PIMS Site Director at the University of Lethbridge site. He also serves on the PIMS Digital Collaboration Committee.

His main area of research is analytic number theory. He is interested in the Riemann zeta function, L-functions, prime numbers, and a variety of problems in multiplicative number theory. His Ph.D. thesis, "Limiting Distributions and Zeros of Artin L-functions", studied the finer behaviour of the summatory function of the Mobius function and Chebyshev's bias in Galois groups. Some research topics he works on include: mean values of L-functions, non-vanishing of L-functions, 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 distribution functions of number theoretic functions. Recently, he has been interested in questions concerning simple zeros of L-functions and linear combinations of zeros of L-functions. For more information please see his research page .

The prime number theorem proven independently by de la Vallée Poussin and Hadamard (1896) is an asymptotic statement about prime counting functions. It holds for sufficiently large numbers x. In 1941 Rosser authored an article giving explicit...

The “Comparative Prime Number Theory” symposium is one of the highlight events organized by the PIMS-funded Collaborative Research Group (CRG) “ L-functions in Analytic Number Theory”. It is a one-week event taking place on the UBC campus in...

Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester. EVERYONE IS WELCOME!

The 2k-th moments I_k(T) of the Riemann zeta function have been studied extensively. In the late 90's, Keating-Snaith gave a conjecture for the size of I_k(T). At the same time Conrey-Gonek connected I_k(T) to mean values of long Dirichlet...

In this talk I will consider the discrete moments J_k(T) that are defined by summing the 2k-th power of the absolute value of the derivative of the Riemann zeta function zeta(s) at all nontrivial zeros of zeta(s) whose imaginary part has absolute...

In the past twenty years there has been a flurry of activity in the study of mean values of L-functions. This was precipitated by groundbreaking work of Keating and Snaith in which they modelled these mean values by random matrix theory. In this talk...

A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$. For $T \ge 1$, the mean values $$\int_{0}^{T} |A(t)|^2 \, dt$$ play an important role in...

A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$. For $T \ge 1$, the mean values$$\int_{0}^{T} |A(t)|^2 \, dt$$play an important role in...

Hardy and Littlewood initiated the study of the 2k-th moments of the Riemann zeta function on the critical line. In 1918 Hardy and Littlewood established an asymptotic formula for the second moment and in 1926 Ingham established an asymptotic formula...

Let f be a primitive modular form and L(s) its associated L-function. Anton Good (1982) bounded |L(s)| by approximately the cube root of the distance from the real axis on the line s = 1/2, in the case f is a modular form on the full modular group...