De partitiefunctie van Rademacher

De partitiefunctie van Rademacher

Ros, Robin (TU Delft Electrical Engineering, Mathematics and Computer Science)

Bosman, Johan (mentor)
van den Dries, Bart (graduation committee)
Gijswijt, Dion (graduation committee)

Delft University of Technology

2018-07-09

There are several ways to write the number 5 as a sum of positive integers, disregarding order. A quick calculation shows that this can be done in 7 ways: 5 = 5, 5 = 4 + 1, 5 = 3 + 2, 5 = 3 + 1 + 1, 5 = 2 + 2 + 1, 5 = 2 + 1 + 1 + 1 and 5 = 1 + 1 + 1 + 1 + 1. In the same way, we can count the number of ways for each integer n. Although this calculation is trivial, a closed form for this function is not as easily obtained as one for combinations, for example. This work formulates and proves Rademacher's formula for these partition numbers. It also tries to uncover some key ideas behind the proof, the supporting theory and other inspirations.

Partition
Rademacher
Circle method
Ford-circles
Farey-sequences
Hardy
Ramanujan

http://resolver.tudelft.nl/uuid:93f83559-9ffa-44e1-876a-aa0d561ee1a5

Student theses

bachelor thesis

© 2018 Robin Ros