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 CMFD, 2013, Volume 49, Pages 132–164 (Mi cmfd249)

Development of the Valiron–Levin theorem on the least possible type of entire functions with a given upper $\rho$-density of roots

A. Yu. Popov

M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: An entire function such that its roots have a given $\rho$-density and are located in an angle or on a ray is considered. For such a function, we solve the problem on the least possible type at order $\rho$. The case without assumptions about the location of the roots was considered by Valiron; the corresponding problem was completely solved by Levin.

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English version:
Journal of Mathematical Sciences, 2015, 211:4, 579–616

UDC: 517.5

Citation: A. Yu. Popov, “Development of the Valiron–Levin theorem on the least possible type of entire functions with a given upper $\rho$-density of roots”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 49, PFUR, M., 2013, 132–164; Journal of Mathematical Sciences, 211:4 (2015), 579–616

Citation in format AMSBIB
\Bibitem{Pop13} \by A.~Yu.~Popov \paper Development of the Valiron--Levin theorem on the least possible type of entire functions with a~given upper $\rho$-density of roots \inbook Proceedings of the Crimean autumn mathematical school-symposium \serial CMFD \yr 2013 \vol 49 \pages 132--164 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd249} \transl \jour Journal of Mathematical Sciences \yr 2015 \vol 211 \issue 4 \pages 579--616 \crossref{https://doi.org/10.1007/s10958-015-2618-8} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84946496697} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. G. G. Braichev, “Sharp Estimates of Types of Entire Functions with Zeros on Rays”, Math. Notes, 97:4 (2015), 510–520
2. G. G. Braichev, “The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities”, Ufa Math. J., 7:4 (2015), 32–57
3. G. G. Braichev, “The least type of an entire function whose zeros have prescribed averaged densities and lie on rays or in a sector”, Sb. Math., 207:2 (2016), 191–225
4. V. B. Sherstyukov, “Minimal value for the type of an entire function of order $\rho\in(0,1)$, whose zeros lie in an angle and have a prescribed density”, Ufa Math. J., 8:1 (2016), 108–120
5. V. B. Sherstyukov, G. G. Braichev, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97
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