ISSN:
1420-8903
Keywords:
Primary 11K65
;
Secondary 11N37, 11A25, 43A60
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Still another proof is given for Parseval's well-known equation $$\sum\limits_{1 \leqslant r〈 \infty } {|a_r |^2 \cdot \varphi (r) = \parallel f\parallel \begin{array}{*{20}c} 2 \\ 2 \\ \end{array} } $$ forB 2-almost-even arithmetical functionsf with Ramanujan coefficients $$a_r = \frac{1}{{\varphi (r)}} \cdot M(f \cdot c_r )$$ . An explicit “best approximation” off by even functions, constructed from characteristic functions of subsets {n; g.c.d.(n, r) =k} ⊂ $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{\mathbb{N}} $$ is used.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01830940
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