Geodesic
Arithmetical aspects of certain functional equations
Acta Arithmetica, Tome 82 (1997) no. 3, pp. 257-277

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The classical system of functional equations      $ 1/n ∑_{ν=0}^{n-1} F((x+ν)/n) = n^{-s} F(x)$ (n ∈ ℕ) with s ∈ ℂ, investigated for instance by Artin (1931), Yoder (1975), Kubert (1979), and Milnor (1983), is extended to      $ 1/n ∑_{ν=0}^{n-1} F((x+ν)/n) = ∑_{d=1}^∞ λ_n(d)F(dx)$ (n ∈ ℕ) with complex valued sequences $λ_n$. This leads to new results on the periodic integrable and the aperiodic continuous solutions F:ℝ₊ → ℂ interrelating the theory of functional equations and the theory of arithmetic functions.
DOI : 10.4064/aa-82-3-257-277

Lutz Lucht 1

1 
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Lutz Lucht. Arithmetical aspects of certain functional equations. Acta Arithmetica, Tome 82 (1997) no. 3, pp. 257-277. doi: 10.4064/aa-82-3-257-277

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