# On a property of pairs of almost periodic zero sets

Author
Karazin Kharkiv National University
Abstract
Whenever all differences of zeros of two holomorphic almost periodic functions in a strip form a discrete set, then both functions are infinite products of periodic functions with commensurable periods. In particular, the result is valid for some classes of Dirichlet series.
Keywords
quasipolynomial; periodic function; zero set; Dirichlet series; almost periodic holomorphic function
DOI
doi:10.15330/ms.43.1.43-50
Reference
1. S.Ju. Favorov, N.P. Girya, On a criterion of periodicity of polynomials, Ufa’s Mathematical Journal, 4 (2012), ¹1, 47–52.

2. S.Yu. Favorov, A.Yu. Rashkovskii, A.I. Ronkin, Almost periodic divisors in a strip, J. d’Analyse Math., 74 (1998), 325–345.

3. N.P. Girya, Periodicity of Dirichlet series, Mat. Stud., 42 (2014), ¹1, 13–18.

4. B. Jessen, H. Tornehave, Mean motions and zeros of almost periodic functions, Acta Math., 77 (1945), 137–279.

5. M.G. Krein, B.Ja. Levin, On entire almost periodic functions of an exponential type, DAN SSSR, 64 (1949), ¹2, 285–287. (in Russian)

6. B.Ja. Levin, Distributions of zeros of entire functions, V.5, Transl. of Math. Monograph, AMS Providence, R1, 1980.

7. B.M. Levitan, Almost periodic functions, Gostehizdat, Moscow, 1953. (in Russian)

8. H. Tornehave, Systems of zeros of holomorphic almost periodic functions, Kobenhavns Universitet Matematisk Institut, Preprint, ¹30, 1988.

Pages
43-50
Volume
43
Issue
1
Year
2015
Journal
Matematychni Studii
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