Abel Summation of Ramanujan-Fourier Series

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).

13 pages. No Figures. Updated the definitions and made the theorem on uniform convergence more explicit

References in corpus (4)

• Linking the Circle and the Sieve: Ramanujan - Fourier Series
• Ramanujan - Fourier Series and the Density of Sophie Germain Primes
• Rota meets Ramanujan: Probabilistic interpretation of Ramanujan - Fourier series
• Convolution and Cross-Correlation of Ramanujan-Fourier Series

Cited by in corpus (1)

• On a Mean Value of Gadiyar and Padma