About a month ago, I emailed a potential PhD advisor in the field of theoretical physics expressing my interest in a PhD position he had advertised. He replied back by saying that he normally gives a problem set for PhD applicants to solve within 2 days. A week later, while sending me the questions, he added that he wanted to understand how reliable I am with calculations. The problem set included questions of increasing difficulty. I solved the problem set in the specified deadline and sent back the solutions but he hasn't replied since then.
Should I send him a reminder email to know the status of my application process?