Greg Knapp

Number Theory

Most of my research attention is devoted to number theory from an analytic perspective (which is different from analytic number theory), where my interests include diophantine approximation, root separation of polynomials, height functions, the geometry of numbers, and other topics.  My advisor is Shabnam Akhtari.

My research statement is here.


The Number of Solutions to the Trinomial Thue Equation. arXiv preprint.  Accepted for publication in Functiones et Approximatio Commentarii Mathematici.
Here is the associated Jupyter notebook: trinomial_computations.ipynb
Here are the .csv files containing data about the number of solutions to trinomial Thue equations of fixed degree and height:


I have given several versions of the same talk on my research into Thue equations.  All have been titled something like "Bounds on the Number of Solutions to Thue's Inequality."  The slides for the best version of the talk (which will be given in the Oregon State number theory seminar on February 7, 2023) are here: thue_equation_talk.pdf

I will also be speaking at the upcoming Oregon Number Theory Days conference about some of my work on root separation of polynomials.  Slides will be posted when they are ready.


I did my master's thesis under Colin McLarty at Case Western Reserve University in 2017.  I am currently working on completing some of the finer details with Zach Jandrasi and I hope to publish the results some time in 2022.

"Minkowski's Linear Forms Theorem in Elementary Function Arithmetic." Electronic Thesis or Dissertation. Case Western Reserve University, 2017. OhioLINK Electronic Theses and Dissertations Center.