# 2003 Research Experiences for Undergraduates

Computational Number Theory and Combinatorics

Research Projects

** Please note that some of these works are still in progress! **

## Lang-Trotter Conjecture group

This group consisted of Rebecca Bilbro and Eric Manley and was
supervised by Kevin James.
They implemented algorithms to quickly compute the number of points on a
given elliptic curve over a finite field with p elements. They used
these algorithms to gather extensive data related to the Lang-Trotter
conjecture.

Lang-Trotter Investigation Report

## Class Number Group

This group consisted of Brittany Brown and Amy Stout and was supervised
by Tim Flowers and Kevin James.
They wrote Pari code to compute various sums of Hurwitz-Kronecker class
numbers. They studied this data and were led to conjecture formulas for
these sums of class numbers. They were then able to prove a couple of
these conjectures.
Sums of Class Numbers Report

## l-Regular Partition Function Group

This group consisted of Christian Bruun and Chip Swannack and was
supervised by Neil Calkin and Kevin James. Christian gathered extensive
data on l-regular partition functions and used this data to study
various conjectures of Ken Ono and David Penniston.
l-Regular Partitions Report

## Coupon Collector Problems Group

This group consisted of Lee Gilman, Natalie Hudson, Rhett Robinson and
Dana walker and was supervised by Neil Calkin and Shannon Purvis. They
analyzed the probability of collecting c copies of all n baseball cards,
assuming uniform distribution, after t trials of collecting r unique
cards at a time. They were able to generate some closed formulas based
on a combinatorial analysis and are still working on asymptotics.
Coupon Collector Report