Periodicity of Dirichlet series 

Author 
n girya@mail.ru
Karazin Kharkiv National University

Abstract 
We prove that whenever all differences between zeros of two quasipolynomials form a discrete
set, then both quasipolynomials are periodic with the same period. The result is valid for some
classes of Dirichlet series and almost periodic holomorphic functions as well.

Keywords 
quasipolynomial; periodic function; zero set; discrete set; Dirichlet series; almost periodic
holomorphic function

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. G. Kozma, F. Oravecz, On the gaps between zeros of trigonometric polynomials, Real Anal. Exchange, 28 (2002/03), ¹2, 447–454. 3. M.G. Krein, B.Ja. Levin, On entire almost periodic functions of an exponential type, DAN SSSR, 64 (1949), ¹2, 285–287. (in Russian) 4. B.Ja. Levin, Distributions of zeros of entire functions, V.5, Transl. of Math. Monograph, AMS Providence, R1, 1980. 5. V.P. Potapov, On divisors of quasipolynomials, Sbornik trudov Instituta matematiki AN SSSR, ser. mat, 6 (1942), 115–134. (in Russian) 6. B.M. Levitan, Almost periodic functions, Gostehizdat, Moscow, 1953. (in Russian) 
Pages 
3843

Volume 
42

Issue 
1

Year 
2014

Journal 
Matematychni Studii

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