The Arithmetic Fourier Transform
Complex Variables
2020-12-15 v1 Number Theory
Abstract
The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and can be performed by parallel processing. The AFT has some deep connections with the Prime Number Theorem and its rich history is discussed in this expository article.
Cite
@article{arxiv.2012.06963,
title = {The Arithmetic Fourier Transform},
author = {Joel L. Schiff},
journal= {arXiv preprint arXiv:2012.06963},
year = {2020}
}
Comments
23 pages. Dedicated to my colleague Wayne J. Walker (1944-2019). Together we uncovered some of the beautiful aspects of the AFT