The Laguerre inequality and the distribution of zeros of entire functions
Csordas, George ; Escassut, Alain
Annales mathématiques Blaise Pascal, Tome 12 (2005), p. 331-345 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

@article{AMBP_2005__12_2_331_0,
     author = {Csordas, George and Escassut, Alain},
     title = {The Laguerre inequality and the distribution of zeros of entire functions},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {12},
     year = {2005},
     pages = {331-345},
     doi = {10.5802/ambp.210},
     zbl = {1096.30023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2005__12_2_331_0}
}

Csordas, George; Escassut, Alain. The Laguerre inequality and the distribution of zeros of entire functions. Annales mathématiques Blaise Pascal, Tome 12 (2005) pp. 331-345. doi : 10.5802/ambp.210. http://gdmltest.u-ga.fr/item/AMBP_2005__12_2_331_0/

[1] Boas, R.P. Entire Functions, Academic Press, New York (1954) | MR 68627 | Zbl 0058.30201

[2] Cardon, D. A.; De Gaston, S. A. Differential operators and entire functions with simple real zeros, J. Math. Anal. Appl., Tome 301 (2005), pp. 286-393 | Article | MR 2105679 | Zbl 1066.30031

[3] Craven, T.; Csordas, G. Differential operators of infinite-order and the distribution of zeros of entire functions, J. Math. Anal. Appl., Tome 186 (1994), pp. 799-820 | Article | MR 1293856 | Zbl 0810.30006

[4] Csordas, G.; Varga, R. S. Necessary and sufficient conditions and the Riemann Hypothesis, Adv. in Appl. Math., Tome 11 (1990), pp. 328-357 | Article | MR 1061423 | Zbl 0707.11062

[5] De Bruijn, N.G. The roots of Trigonometric integrals, Duke Math, Tome 7 (1950), pp. 197-226 | Article | MR 37351 | Zbl 0038.23302

[6] G. Csordas, W. Smith; Varga, R. S. Level sets of real entire functions and the Laguerre inequalities, Analysis, Tome 12 (1992), pp. 377-402 | MR 1182637 | Zbl 0759.30016

[7] Jensen, J. L. W. V. Recherches sur la théorie des équations, Acta Math., Tome 36 (1913), pp. 181-195 | Article | JFM 43.0158.01 | MR 1555086

[8] Kuipers, L. Note on the location of zeros of polynomials, Simon Stevin, Tome 31 (1957), pp. 61-72 | MR 83970 | Zbl 0082.02203

[9] Levin, B. Ja. Distribution of Zeros of Entire Functions, Transl. Math. Mono. Vol 5. Amer. Math. Soc, Providence, R.I. (1980) | MR 589888

[10] Obreschkoff, N. Verteilung und Berechnung der Nullstellen reeller Polynome, VEB Deutscher Verlag der Wissenschaften, Berlin (1963) | MR 164003 | Zbl 0156.28202

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

[12] Pólya, G. Location of Zeros, Collected papers, Vol.2, R.P. Boas, MIT Press, Cambridge, MA (1974) | MR 505093

[13] Sikkema, P. C. Differential Operators and Differential Equations of Infinite Order with Constant Coefficients, P. Noordhoff N.V., Groningen (1953) | MR 60082 | Zbl 0051.34402