NOTE: This talk will be independent of the similarly titled talk in the RTG seminar and will focus more on the proofs of the main results.

Title: Number theoretic applications of a class of Cantor series fractal functions part 1

Abstract: We will introduce a new class of Cantor series fractal functions and discuss their applications to problems involving normal numbers and computation of the Hausdorff dimension of certain sets defined through digital restrictions. In particular, we will discuss how these functions may be used to reduce the problem of constructing normal numbers with certain pathological properties to solving systems of Diophantine relations. Multifractal analysis of these functions will be given and we will study their continuity, behavior on rational points, and several other properties.