On some solutions of a functional equation related to the partial sums of the Riemann zeta function
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http://hdl.handle.net/10045/35671
Títol: | On some solutions of a functional equation related to the partial sums of the Riemann zeta function |
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Autors: | Sepulcre, Juan Matias |
Grups d'investigació o GITE: | Curvas Alpha-Densas. Análisis y Geometría Local |
Centre, Departament o Servei: | Universidad de Alicante. Departamento de Análisis Matemático |
Paraules clau: | Functional equations | Space-filling curves | Partial sums of the Riemann zeta function | Alpha-dense curves | Property of quadrature |
Àrees de coneixement: | Análisis Matemático |
Data de publicació: | 1-de gener-2014 |
Editor: | Korean Mathematical Society |
Citació bibliogràfica: | Bulletin of the Korean Mathematical Society. 2014, 51(1): 29-41. doi:10.4134/BKMS.2014.51.1.029 |
Resum: | 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. |
Patrocinadors: | 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 |
Idioma: | eng |
Tipus: | info:eu-repo/semantics/article |
Drets: | © 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. |
Revisió científica: | si |
Versió de l'editor: | http://dx.doi.org/10.4134/BKMS.2014.51.1.029 |
Apareix a la col·lecció: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
Arxius per aquest ítem:
Arxiu | Descripció | Tamany | Format | |
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2014_Sepulcre_BullKoreanMathSoc.pdf | 163,52 kB | Adobe PDF | Obrir Vista prèvia | |
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