Artin's primitive root conjecture -a survey -

This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background. The talk covered some of the history, results and ideas connected with Artin's celebrated primitive root conjecture dating from 1927. In the update several new results established after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer

Around the p-adic Littlewood Conjecture

In this dissertation, we look at the Littlewood Conjecture and several related open problems. We introduce notions and theorems from various fields in order to properly formulate the conjectures and properly state the various results related to them. In Chapter 5, we investigate a potential counter-example to the p-adic Littlewood conjecture when p=2 via an intricate construction, and show that this potential counter-example does indeed satisfy the premises of the conjecture