What is the ruling on placing loudspeakers on the rooftops of houses in residential areas to emit sounds such as prayers upon the Prophet, glorification of God (Tasbeeh), and seeking forgiveness (Istighfar)?

The remembrance of Allah (Dhikr) and reminding others of Him are permissible, but they must not cause harm to Muslims. If playing Dhikr through loudspeakers causes harm to neighbors, such as the sick or students, then it is not permissible.