Geodesic
The poles of Padé approximants to $_1F_1(1;c;z)$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1982), pp. 11-14 
D. V. Pannikov. The poles of Padé approximants to $_1F_1(1;c;z)$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1982), pp. 11-14. http://geodesic.mathdoc.fr/item/VMUMM_1982_1_a2/
@article{VMUMM_1982_1_a2,
     author = {D. V. Pannikov},
     title = {The poles of {Pad\'e} approximants to $_1F_1(1;c;z)$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {11--14},
     year = {1982},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_1_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We construct some regions without zeros of the confluent hypergeometric function $_1F_1(-n;d;z)$ ($n\in\mathbf N, d\in\mathbf C$). The main result is as follows. If $$ -n+\frac7{16}\geq\operatorname{Re}(d),\quad_1F_1(-n;d;z)=0, $$ then $$ -\operatorname{Re}(d)-\operatorname{Im}(d)\operatorname{tg}\biggl(\frac{\arg(z)}2\biggr) \geq|z|>\operatorname{Re}(z)+2\biggl(-n+\frac7{16}- \operatorname{Re}(d)\biggr). $$