# De partitiefunctie van Rademacher

De partitiefunctie van Rademacher

AuthorRos, 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

Date2018-07-09

AbstractThere 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.

SubjectPartition

Rademacher

Circle method

Ford-circles

Farey-sequences

Hardy

Ramanujan

Student theses

Document typebachelor thesis

Rights© 2018 Robin Ros