In this paper we prove that the shifted Hermite polynomial $H_{n}(x)+b$ has at least three simple zeros for each complex number $b$, provided that $n\geq 7$.
@article{1269437064,
author = {Rakaczki, Csaba},
title = {On some diophantine results related to Hermite polynomials},
journal = {Funct. Approx. Comment. Math.},
volume = {42},
number = {1},
year = {2010},
pages = { 7-16},
language = {en},
url = {http://dml.mathdoc.fr/item/1269437064}
}
Rakaczki, Csaba. On some diophantine results related to Hermite polynomials. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp. 7-16. http://gdmltest.u-ga.fr/item/1269437064/