On some solutions of a functional equation related to the partial sums of the Riemann zeta function

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Title: On some solutions of a functional equation related to the partial sums of the Riemann zeta function
Authors: Sepulcre, Juan Matias
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Functional equations | Space-filling curves | Partial sums of the Riemann zeta function | Alpha-dense curves | Property of quadrature
Knowledge Area: Análisis Matemático
Issue Date: 1-Jan-2014
Publisher: Korean Mathematical Society
Citation: Bulletin of the Korean Mathematical Society. 2014, 51(1): 29-41. doi:10.4134/BKMS.2014.51.1.029
Abstract: In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, 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 nth power of the density approaches the Jordan content of the compact set which the curve densifies.
Sponsor: The author was partially supported by Vicerrectorado de Investigación, Desarrollo e Innovación de la Universidad de Alicante under project GRE11-23.
URI: http://hdl.handle.net/10045/35671
ISSN: 1015-8634 (Print) | 2234-3016 (Online)
DOI: 10.4134/BKMS.2014.51.1.029
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Korean Mathematical Society. The person using Bulletin of the Korean Mathematical Society Online may use, reproduce, disseminate, or display the open access version of content from this journal for non-commercial purposes.
Peer Review: si
Publisher version: http://dx.doi.org/10.4134/BKMS.2014.51.1.029
Appears in Collections:INV - CADAGL - Artículos de Revistas

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