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Still another proof of Parseval's equation for almost-even arithmetical functions (1988)

Hildebrand, Adolf ; Schwarz, Wolfgang ; Spilker, Jürgen

Springer

Aequationes mathematicae 35 (1988), S. 132-139

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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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