The Laguerre inequality and the distribution of zeros of entire functions
Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 2, pp. 331-345.

The Laguerre inequality and the distribution of zeros of real entire functions are investigated with the aid of certain infinite-order differential operators. The paper includes new proofs, problems, conjectures and many illustrative examples and counterexamples.

DOI: 10.5802/ambp.210
George Csordas 1; Alain Escassut 2

1 University of Hawaii Department of Mathematics Honolulu, HI 96822 USA
2 Université Blaise Pascal Laboratoire de Mathematiques Les Cézaux 63177 Aubiere Cedex FRANCE
@article{AMBP_2005__12_2_331_0,
     author = {George Csordas and Alain Escassut},
     title = {The {Laguerre} inequality and the distribution of zeros of entire functions},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {331--345},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {12},
     number = {2},
     year = {2005},
     doi = {10.5802/ambp.210},
     zbl = {1096.30023},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.210/}
}
TY  - JOUR
AU  - George Csordas
AU  - Alain Escassut
TI  - The Laguerre inequality and the distribution of zeros of entire functions
JO  - Annales mathématiques Blaise Pascal
PY  - 2005
SP  - 331
EP  - 345
VL  - 12
IS  - 2
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.210/
DO  - 10.5802/ambp.210
LA  - en
ID  - AMBP_2005__12_2_331_0
ER  - 
%0 Journal Article
%A George Csordas
%A Alain Escassut
%T The Laguerre inequality and the distribution of zeros of entire functions
%J Annales mathématiques Blaise Pascal
%D 2005
%P 331-345
%V 12
%N 2
%I Annales mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.210/
%R 10.5802/ambp.210
%G en
%F AMBP_2005__12_2_331_0
George Csordas; Alain Escassut. The Laguerre inequality and the distribution of zeros of entire functions. Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 2, pp. 331-345. doi : 10.5802/ambp.210. https://ambp.centre-mersenne.org/articles/10.5802/ambp.210/

[1] R.P. Boas Entire Functions, Academic Press, New York, 1954 | MR | Zbl

[2] D. A. Cardon; S. A. de Gaston Differential operators and entire functions with simple real zeros, J. Math. Anal. Appl., Volume 301 (2005), pp. 286-393 | DOI | MR | Zbl

[3] T. Craven; G. Csordas Differential operators of infinite-order and the distribution of zeros of entire functions, J. Math. Anal. Appl., Volume 186 (1994), pp. 799-820 | DOI | MR | Zbl

[4] G. Csordas; R. S. Varga Necessary and sufficient conditions and the Riemann Hypothesis, Adv. in Appl. Math., Volume 11 (1990), pp. 328-357 | DOI | MR | Zbl

[5] N.G. de Bruijn The roots of Trigonometric integrals, Duke Math, Volume 7 (1950), pp. 197-226 | DOI | MR | Zbl

[6] W. Smith G. Csordas; R. S. Varga Level sets of real entire functions and the Laguerre inequalities, Analysis, Volume 12 (1992), pp. 377-402 | MR | Zbl

[7] J. L. W. V. Jensen Recherches sur la théorie des équations, Acta Math., Volume 36 (1913), pp. 181-195 | DOI | JFM | MR

[8] L. Kuipers Note on the location of zeros of polynomials, Simon Stevin, Volume 31 (1957), pp. 61-72 | MR | Zbl

[9] B. Ja. Levin Distribution of Zeros of Entire Functions, Transl. Math. Mono. Vol 5. Amer. Math. Soc, Providence, R.I., 1980 | MR

[10] N. Obreschkoff Verteilung und Berechnung der Nullstellen reeller Polynome, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963 | MR | Zbl

[11] G. Pólya Über die algebraisch-funktionentheoretischen Untersuchungen von J. L. W. V. Jensen, Klg. Danske Vid. Sel. Math.-Fys. Medd, Volume 7 (1927), pp. 3-33

[12] G. Pólya Location of Zeros, Collected papers, Vol.2, R.P. Boas, MIT Press, Cambridge, MA, 1974 | MR

[13] P. C. Sikkema Differential Operators and Differential Equations of Infinite Order with Constant Coefficients, P. Noordhoff N.V., Groningen, 1953 | MR | Zbl

Cited by Sources: