Journal of Undergraduate Research
Keywords
Poincaré series, modular form, complex-valued functions
College
Physical and Mathematical Sciences
Department
Mathematics
Abstract
Introduction Poincaré series are a certain type of modular form. Modular forms are complex-valued functions that satisfy certain symmetry properties. There are many different types of modular forms, and one way to classify modular forms is by their level, such as 1, 2, 3, etc. They are of much interest as a research subject because they are connected in surprising ways to many different fields in number theory—e.g., elliptic curves, quadratic forms, and partition functions, to name just a few. As we gain more insight into the various properties of modular forms, we gain more insight into how these various branches of number theory are connected.
Recommended Citation
Haddock, Andrew and Jenkins, Paul
(2015)
"Zeros of Poincare Series of Level 2,"
Journal of Undergraduate Research: Vol. 2015:
Iss.
1, Article 204.
Available at:
https://scholarsarchive.byu.edu/jur/vol2015/iss1/204