Abel Summation of Ramanujan-Fourier Series
Number Theory
2015-12-08 v7
Abstract
Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions. The main result is that the convolution of most arithmetic functions possessing an R-F expansion are Abel-summable to a result involving only the Ramanujan-Fourier coefficients of the R-F expansion(s).
Keywords
Cite
@article{arxiv.1309.2716,
title = {Abel Summation of Ramanujan-Fourier Series},
author = {John Washburn},
journal= {arXiv preprint arXiv:1309.2716},
year = {2015}
}
Comments
13 pages. No Figures. Updated the definitions and made the theorem on uniform convergence more explicit