On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function |
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Authors: | G Mora JM Sepulcre |
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Affiliation: | Department of Mathematical Analysis, University of Alicante, 03080-Alicante, Spain |
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Abstract: | In this paper we study the distribution of zeros of each entire function of the sequence , which approaches the Riemann zeta function for Rez<−1, and is closely related to the solutions of the functional equations f(z)+f(2z)+?+f(nz)=0. We determine the density of the zeros of Gn(z) on the critical strip where they are situated by using almost-periodic functions techniques. Furthermore, by using a theorem of Kronecker, we also establish a formula for the number of zeros of Gn(z) inside certain rectangles in the critical strip. |
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Keywords: | Zeros of entire functions Almost-periodic functions Functional equations |
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