Anna Hall, Bachelor's thesis, K37

Date and time: Friday 12/12, 14:30
Place: Cramér meeting room, Albano building 1
Student: Anna Hall
Supervisor: Salvador Rodriguez Lopez
Title: "The Zeta function and The Prime Number Theorem"

Abstract

The aim of this thesis is to investigate certain important properties of the Zeta function in the complex plane and use those to give a proof of The Prime Number Theorem. To do so we utilise the concept of analytic continuation, properties of the Gamma function, and briefly the Bernoulli numbers. In Chapter 1, we prove that the Gamma and Zeta functions are meromorphic in the complex plane, show different ways of representing the Zeta function, and end by investigating this function near the line Re(s)=1 in the complex plane. In Chapter 2, we utilise the results of Chapter 1 to look at the growth of the Zeta function near that same line, and together with Chebychev's Psi functions we prove two propositions and a theorem that together form the Prime Number Theorem. After the main chapters, we have Appendix A that covers the mathematical basis of analytic continuation and Appendix B which covers important concepts that are referred to in Chapters 1 and 2.

More presentations the same week

Maximilian Vranjes, Bachelor's thesis, K38

Date and time: Monday 8/12, 12:30
Place: Mittag-Leffler meeting room, Albano building 1
Student: Maximilian Vranjes
Supervisor: Anders Mörtberg
Title: "The Proofs of the Compactness Theorem of First Order Logic"

Simon Hanson, Bachelor's thesis, K35

Date and time: Monday 8/12, 14:00
Place: Cramér meeting room, Albano building 1
Student: Simon Hanson
Supervisor: Jonas Bergström
Title: "Hilbert's Invariance Theorem"

Zahra Alimoradzadeh, Master's thesis, M10

Date and time: Thursday 11/12, 8:30
Place: Cramér meeting room, Albano building 1
Student: Zahra Alimoradzadeh
Supervisor: Yishao Zhou
Title: "Asymptotic Analysis and Comparison of Model-Based and Model-Free Methods for the Linear Quadratic Regulator"

Andreas Karlsson, Bachelor's thesis, K36

Date and time: Thursday 11/12, 13:00
Place: Mittag-Leffler meeting room, Albano building 1
Student: Andreas Karlsson
Supervisor: Annemarie Luger
Title: "Machine Learning in Kreĭn Spaces: An Exposition to the Main Representer Theorems"

For abstracts, see the department's calendar