BYU math professor Paul Jenkins’ passion lies in helping students find their own research projects to work on.

“It’s been a really rewarding thing to be involved in mentoring,” Jenkins said. “It’s been one of the most rewarding parts of being on the faculty here.”

When he was an undergraduate at BYU (BS ’00, Mathematics), Jenkins became interested in mathematics when his Number Theory professor David Clark helped him get involved in a research project.

“I loved the experience of doing research as an undergraduate,” Jenkins said. “When I came back here as a faculty member, this was something I was excited to do: to work with the great students we have here and help them get involved in research.”

For his latest research project, Jenkins worked closely with recent graduate Kyle Pratt. Together, they tackled the challenge of finding coefficient bounds for modular functions.

“The idea mathematically is that for certain mathematical objects, called modular forms, one question you can ask is how quickly the coefficients grow,” Jenkins said.

Jenkins had found the coefficient bounds for a certain set of modular forms in previous research, but he and Pratt wanted to extend those results to a larger class of modular forms.

“It was a natural question,” Jenkins said. “We had done it for the easiest case, but the question was whether these results were still true as you looked at more complicated examples.”

Pratt was a coauthor on the paper Jenkins published. Jenkins said that Pratt’s work on the project was beyond what he’d expected of an undergraduate student.

“I was extremely impressed with what he was able to do,” Jenkins said. “I think it really prepared him well for the graduate work that he’s doing.”