Abstract
By using known asymptotics of the counting function of zeros of an entire functionf of order zero, we determine the asymptotics of Inf under the condition that all zeros off lie on the same ray. The inverse problem is also analyzed.
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References
G. Valiron, “Sur les fonctions entiéres d’ordre nul et d’ordre fini et en particulier les fonctions á correspondance réguliére,”Ann. Fac. Sci. Univ. Toulouse,5, 117–257 (1914).
E. G. Titchmarsh, “On integral functions with real negative zeros,”Proc. London Math. Soc.,26, No. 2, 185–200 (1927).
V. N. Logvinenko, “On entire functions with zeros on a half line. I,”Teor. Funkts., Funkts. Anal. Prilozhen., Issue 16, 154–158 (1972).
V. N. Logvinenko, “On entire functions with zeros on a half line. II,”Teor. Funkts., Funkts. Anal. Prilozhen., Issue 17, 84–99 (1973).
M. M. Tyan, “One application of the Tauberian theorem of Carleman and Subkhankulov,”Izv. Akad. Nauk Uzbek SSR, Ser. Fiz.-Mat., No. 3, 18–20(1963).
M. V. Keldysh, “On one Tauberian theorem,”Tr. Mat. Inst. Akad. Nauk SSSR,38, 77–86 (1951).
M. A. Subkhankulov,Tauberian Theorems with Remainders [in Russian], Nauka, Moscow 1976.
B. I. Korenblyum, “General Tauberian theorem for ratios of functions,”Dokl Akad. Nauk SSSR,88, No. 5, 745–748 (1953).
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Zabolotskii, M.V. Valiron-type and valiron-titchmarsh-type theorems for entire functions of order zero. Ukr Math J 48, 354–366 (1996). https://doi.org/10.1007/BF02378526
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DOI: https://doi.org/10.1007/BF02378526