2008/05/02 by John Washburn, Washburn, John · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #math.NT #msc:11A41 #msc:11L03 #msc:11L07 #msc:42A32
paper · pdf · doi:10.48550/arxiv.0805.0284
The paper fails to establish the continuity of the a.p. functions involved required to uniformly approximate the a.p. function with the Bochner-Fejer polynomials. Without this uniform convergence the key interchange of limits is not justified
arxiv created 2015/07/28 · arxiv updated 2015/07/29
This paper uses the machinery of almost periodic functions to prove that even without uniform convergence the connection between a pair of almost periodic functions and the constants of the associated Fourier series exists for both the convolution and cross-correlation. The general results for two almost periodic functions are narrowed and applied to Ramanujan sums and finally applied to support the specific relation of the Wiener-Khinchin formula for arithemic functions with a Ramanujan-Fourier Series.