Geometric Aspects of Denseness Theorems for Dirichlet Functions
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 25, Issue 4
Abstract
The first theorem related to the denseness of the image of a vertical line Re s = σ0, σ0 > 1 by the Riemann Zeta function has been proved by Harald Bohr in 1911. We argue that this theorem is not really a denseness theorem. Later Bohr and Courant proved similar theorems for the case 1/2 < Re s ≤ 1. Their results have been generalized to classes of Dirichlet functions and are at the origin of a burgeoning field in analytic number theory, namely the universality theory. The tools used in this theory are mainly of an arithmetic nature and do not allow a visualization of the phenomena involved. Our method is based on conformal mapping theory and is supported by computer generated illustrations. We generalize and refine Bohr and Courant results.
Authors and Affiliations
Dorin Ghisa, Andrei Horvat-Marc
Keywords
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- EP ID EP322357
- DOI 10.9734/JAMCS/2017/37947
- Views 83
- Downloads 0
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