The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0
| Contribuinte(s) |
Universidad de Alicante. Departamento de Análisis Matemático Curvas Alpha-Densas. Análisis y Geometría Local |
|---|---|
| Data(s) |
26/06/2014
26/06/2014
01/08/2013
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| Resumo |
This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero. |
| Identificador |
Mediterranean Journal of Mathematics. 2013, 10(3): 1221-1233. doi:10.1007/s00009-012-0237-x 1660-5446 (Print) 1660-5454 (Online) http://hdl.handle.net/10045/38405 10.1007/s00009-012-0237-x |
| Idioma(s) |
eng |
| Publicador |
Birkhäuser |
| Relação |
http://dx.doi.org/10.1007/s00009-012-0237-x |
| Direitos |
The final publication is available at Springer via http://dx.doi.org/10.1007/s00009-012-0237-x info:eu-repo/semantics/openAccess |
| Palavras-Chave | #Functional equations #Zeros of partial sums of the Riemann zeta function #nth characteristic of a real number #Análisis Matemático |
| Tipo |
info:eu-repo/semantics/article |
