 ## Peter Cho-Ho Lam

Department of Mathematics
Simon Fraser University
Burnaby, BC V5A 1S6

Email: chohol (at) sfu (dot) ca

Last Updated: Oct 1, 2018

I am currently a fifth-year Ph.D. student in the Department of Mathematics at Simon Fraser University. My supervisors are Stephen Choi and Peter Borwein.

I completed my M.Sc. in the Department of Mathematics in August 2014 at University of Hong Kong, under the supervision of Kai Man Tsang and Yuk Kam Lau. The title of my master thesis is "Primes of the form $$x^2+Dy^2$$".

I completed my B.Sc. in the Department of Mathematics in August 2012 at Chinese University of Hong Kong.

Here is my curriculum vitae.

### Research Interests

My research focuses on analytic number theory, especially on problems related to primes. Below are some of the problems I am interested in:

1) (Simultaneous) Prime values of polynomials. For example, given two irreducible binary forms $$F(x, y), G(x, y)\in\mathbb{Z}[x, y]$$, are there infinitely many $$\ell, m\in\mathbb{Z}$$ such that both $$F(\ell, m), G(\ell, m)$$ are primes?

2) Average values of arithmetic functions. That includes, for example,$$\sum_{n\le X}f(n),\hspace{5mm}\sum_{\substack{n\le X\\n\equiv a\pmod q}}f(n), \hspace{5mm}\sum_{X < n \le X+H}f(n), \hspace{5mm}\sum_{n\le X}f(P(n))$$ where $$f$$ is some arithmetic function and $$P(n)$$ might be a polynomial sequence or the $$n$$-th prime $$p_n$$, or some combination of both (e.g. $$P(n)=p_n^2+1$$).

3) Analytic methods in other area, e.g. arithmetic geometry, combinatorics.

### Publications

• (With Stephen Choi) Gap principle of polynomial sequences, in preparation.
• (With Damaris Schindler, Stanley Xiao) On prime values of binary quadratic forms with a thin variable, submitted. ArXiv
• Primes of the form $$\alpha x^2+\beta xy+\gamma y^2$$, submitted for publication.
• (With Tsz Ho Chan, Stephen Choi) Divisibility on the sequence of perfect squares minus one: the gap principle, published in Journal of Number Theory, Volume 184, March 2018, p. 473-484. Link
• Representation of Integers Using $$a^2+b^2-dc^2$$, published in J. Integer Seq., 18 (2015), Article 15.8.6. Link

### Data Science

I am currently learning data science and below are some excellent articles I saw:

Did Drought Cause the War in Syria? An R Tutorial by Richard Allen

Deep Learning: An Introduction for Applied Mathematicians by Catherine Higham and Desmond Higham

What is principal component analysis? by Lior Pachter

### An Almost-identity for $$\pi$$

Lennart Berggren, Jonathan Borwein and Peter Borwein discovered the following: this is not an identity but is correct to over 42 billion digits:

$$\bigg(\frac{1}{10^5}\sum_{n=-\infty}^\infty e^{-n^2/10^{10}}\bigg)^2\approx\pi$$

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