The Germany international joined from Chelsea on a five-year deal worth £65m in the summer.
He managed 32 goals in 139 appearances for the Blues, but has so far scored just once in 18 games for Arsenal, prompting onlookers to question if he has improved the team.
"I can tell you that I am really pleased with the way he is performing," said Arteta.
"Looking at just the specific numbers of what he is producing, in front of goal does have to improve and we have to improve them. But in many other areas of the pitch what he gives at the moment is really important."
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