This is the 4284th most frequent French word.
espérant
Hoping.
Here, 'espérant' is used as a participle to describe the action or state of hope while performing another action (sending an email).
Espérant une réponse rapide, il a envoyé un deuxième email.
Hoping for a quick reply, he sent a second email.
In this sentence, 'espérant' is incorrectly used as a verbal noun or participle where 'espérons' (the present tense form of the verb 'espérer') is appropriate.
Nous sommes espérant que les choses s'améliorent bientôt.
We are hoping that things will improve soon.
Here, 'espérant' functions as a present participle indicating the simultaneous action of hoping that occurs during another activity (working).