Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with people gathering in the mosque to offer extra acts of worship like praying tahajjud, reading the Quran and making dhikr during the last ten blessed days of Ramadan.
Answering your question, Sheikh Kifah Mustapha, the Imam and Director of The Prayer Center of Orland Park and representative for Dar El Fatwa of Lebanon in the US, states:
Yes, these are the blessed last ten days of Ramadan in which the prophet (peace be upon him) said the Quran was revealed.
In these last ten days, the special Night of Decree (Laylat al-Qadr) is assumed to be of the odd nights as the prophet (peace be upon him) said: “Seek the Night of Decree in the last ten nights of Ramadan.” (Al-Bukhari)
In another narration, we read: ” Seek the Night of Decree in the last odd nights of the ten days of Ramadan.”
Also, in these last ten days the Prophet used to stay in the mosque for Itikaf. (Muslim) Special prayers like tarawih are performed. Reading Quran and making dhikr are also among the good deeds that one can do in these ten blessed days.
Almighty Allah knows best.