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- W2049361346 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)+<TEX>${cdots}$</TEX>+f(nx) = 0, with <TEX>$n{geq}2$</TEX>, which are related to the partial sums of the Riemann zeta function. These curves <TEX>${alpha}$</TEX>-densify a large class of compact sets of the plane for arbitrary small <TEX>${alpha}$</TEX>, 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 <TEX>$n^{th}$</TEX> power of the density approaches the Jordan content of the compact set which the curve densifies." @default.
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- W2049361346 date "2014-01-31" @default.
- W2049361346 modified "2023-09-29" @default.
- W2049361346 title "ON SOME SOLUTIONS OF A FUNCTIONAL EQUATION RELATED TO THE PARTIAL SUMS OF THE RIEMANN ZETA FUNCTION" @default.
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- W2049361346 doi "https://doi.org/10.4134/bkms.2014.51.1.029" @default.
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