A. Yu. Popov, “On the Least Type of an Entire Function of Order $\rho$ with Roots of a Given Upper $\rho$-Density Lying on One Ray”, Mat. Zametki, 85:2 (2009), 246–260; Math. Notes, 85:2 (2009), 226

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Matematicheskie Zametki, 2009, Volume 85, Issue 2, Pages 246–260
DOI: https://doi.org/10.4213/mzm4645 (Mi mzm4645)

This article is cited in 11 scientific papers (total in 11 papers)

On the Least Type of an Entire Function of Order $\rho$ with Roots of a Given Upper $\rho$-Density Lying on One Ray

A. Yu. Popov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (499 kB) Citations (11)

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DOI: https://doi.org/10.4213/mzm4645

Abstract: It is well known that the least possible type from the class of entire functions of prescribed order $\rho$ with upper root density 1 (for the exponent $\rho$) is $1/(e\rho)$. The author has proved that if all the roots of entire functions lie on one ray, then the situation is different: the least type for such a class on the set of orders $(1,+\infty)\setminus\mathbb N$ is distinct from zero and is bounded above.

Keywords: entire function, least type of an entire function, upper density of a sequence, Lindelöf theorem.

Received: 20.03.2008

English version:
Mathematical Notes, 2009, Volume 85, Issue 2, Pages 226–239
DOI: https://doi.org/10.1134/S000143460901026X

Bibliographic databases:

UDC: 517.547.22

Language: Russian

Citation: A. Yu. Popov, “On the Least Type of an Entire Function of Order $\rho$ with Roots of a Given Upper $\rho$-Density Lying on One Ray”, Mat. Zametki, 85:2 (2009), 246–260; Math. Notes, 85:2 (2009), 226–239

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.4213/mzm4645

https://www.mathnet.ru/eng/mzm/v85/i2/p246

This publication is cited in the following 11 articles:

G. G. Braichev, V. B. Sherstyukov, “On Indicator and Type of an Entire Function with Roots Lying on a Ray”, Lobachevskii J Math, 43:3 (2022), 539
G. G. Braichev, “On the Lower Indicator of an Entire Function with Roots of Zero Lower Density Lying on a Ray”, Math. Notes, 107:6 (2020), 907–919
G. G. Braichev, V. B. Sherstyukov, “Otsenki indikatorov tseloi funktsii s otritsatelnymi kornyami”, Vladikavk. matem. zhurn., 22:3 (2020), 30–46
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
G. G. Braichev, “Sharp Estimates of Types of Entire Functions with Zeros on Rays”, Math. Notes, 97:4 (2015), 510–520
O. V. Sherstyukova, “O naimenshem tipe tselykh funktsii poryadka $\rho\in(0,1)$ s nulyami na luche”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 15:4 (2015), 433–441
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”, Journal of Mathematical Sciences, 211:4 (2015), 579–616
G. G. Braichev, V. B. Sherstyukov, “On the Growth of Entire Functions with Discretely Measurable Zeros”, Math. Notes, 91:5 (2012), 630–644
Braichev G.G., “Sharp bounds for the type of an entire function of order less than 1 whose zeros are located on a ray and have given averaged densities”, Dokl. Math., 86:1 (2012), 559–561
G. G. Braichev, V. B. Sherstyukov, “On the least possible type of entire functions of order $\rho\in(0,1)$ with positive zeros”, Izv. Math., 75:1 (2011), 1–27

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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