This research paper was written by a Senior in high school named Daniel Liu, a USAMO qualifier who had a perfect score on the AMC 10, and is about an inequality called the Reverse Rearrangement inequality which Daniel discovered more than three years ago. In this paper, Daniel shows how his inequality can be used to prove AM-GM in a way never before seen.
We’re going to be switching from a “journal” format to a blog based format. The first article was written by HSJOM editor Catherine Yeo and Dean Cureton during the 2017 REU at Emory University. Their paper discusses the Riemann Hypothesis, one of the most important unsolved problems in mathematics.
Here is a summary of their paper via their abstract.
In this paper…we produce infinite families of polynomials that satisfy the essential expected properties of the Riemann zeta-function. We identify natural families of rational functions in x which are the generating functions for the values of “zeta-polynomials.”
Without further ado here is the article in all it’s mathematical glory. Enjoy!
Polynomials That Behave Like The Riemann Zeta-Function