A Modular Forms Approach to Arithmetic Convoluted Identities

In addition to fulfilling the course and credit requirements, the University of Hawaii’s M.A. in Mathematics program also requires a written paper whose contents are presented to the public.

For this project, I was the author and sole presenter and Dr. Pavel Guerzhoy was my advisor. The goal of my master’s project was to find some interesting mathematical identities using a modular forms approach and to mathematically prove their validity.

What I learned

I learned several several useful skills from this endeavor. Before I proved the general results, I learned to use PARI/GP, a computer algebra system. The program allowed me to verify the first several thousand identities to make sure I was on the right track. I also learned how to create math-oriented slideshows using LaTeX Beamer and honed my presentation skills for public speaking.

You can read the full pdf at A Modular Forms Approach to Arithmetic Convoluted Identities.