Paul Mathieson, 37, was found with serious head and neck injuries in Wilson Street, just after 1am on Sunday January 14.
He was taken by ambulance to the Queen Elizabeth University Hospital in Glasgow but died in the early hours of Saturday January 20.
Police Scotland said that a 26-year-old man has been arrested in connection with the death.
He has been released pending further inquiries.
Police said that inquiries are continuing.