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ON SOME SOLUTIONS OF A FUNCTIONAL EQUATION RELATED TO THE PARTIAL SUMS OF THE RIEMANN ZETA FUNCTION
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 Title & Authors
ON SOME SOLUTIONS OF A FUNCTIONAL EQUATION RELATED TO THE PARTIAL SUMS OF THE RIEMANN ZETA FUNCTION
Martinez, Juan Matias Sepulcre;
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 Abstract
In this paper, we prove that infinite-dimensional vector spaces of -dense curves are generated by means of the functional equations f(x)+f(2x)++f(nx) = 0, with , which are related to the partial sums of the Riemann zeta function. These curves -densify a large class of compact sets of the plane for arbitrary small , extending the known result that this holds for the cases n = 2, 3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the power of the density approaches the Jordan content of the compact set which the curve densifies.
 Keywords
functional equations;space-filling curves;partial sums of the Riemann zeta function;alpha-dense curves;property of quadrature;
 Language
English
 Cited by
1.
On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0, Mediterranean Journal of Mathematics, 2015, 12, 3, 667  crossref(new windwow)
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