On the analytic solutions of the functional equations \(w_1f(a_1z)+w_2f(a_2)z+\dots+w_nf(a_nz=0)\)

DOI10.1007/s00009-014-0444-8zbMath1320.30048OpenAlexW2483830207MaRDI QIDQ493298

Tomás Vidal, Juan Matías Sepulcre

Publication date: 3 September 2015

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-014-0444-8

zbMATH Keywords

functional equationsexponential polynomials

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05)

Related Items (2)

The analytic solutions of the functional equations \(a_1f(\gamma_1 s) + a_2f(\gamma_2 s) + \cdots + a_nf(\gamma_n s) = h(s)\) ⋮ A class of functional equations associated with almost periodic functions

Cites Work

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• The zeros of Riemann zeta partial sums yield solutions to \(f(x)+f(2x)+\cdots+f(nx)=0\)
• The critical strips of the sums \(1+2^{z}+\cdots +n^{z}\)
• Functional equations generating space-densifying curves
• A note on the functional equation \(F(z)+F(2z)+ \cdots +F(nz)=0\)
• On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function
• ON SOME SOLUTIONS OF A FUNCTIONAL EQUATION RELATED TO THE PARTIAL SUMS OF THE RIEMANN ZETA FUNCTION

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