Frank Sinatra was a singer in the 20th century. Brigadier Lethbridge-Stewart was an avowed fan of his. (PROSE: Smash Hit)
Saric Warder began playing a Frank Sinatra tape after picking up Sacha Mary Palmer in his taxi. (PROSE: Trapped!)
One of the items on the Doctor's bucket list was to sing a duet with Sinatra. He eventually do so during his seventh incarnation. Melanie Bush noted that the two of them and Ace were lucky to escape with their lives since Sinatra was less accommodating than the Doctor had hoped. (AUDIO: Maker of Demons)
The Doctor was on close personal terms with Sinatra, using his cabin to hold a party with Albert Einstein and Father Christmas. In 1952, the Eleventh Doctor and Sinatra performed a duet at a Hollywood party. (TV: A Christmas Carol)
The Eighth Doctor, while struggling to recall his memories on Espero, managed to remember the dates of all of Frank Sinatra's comeback tours. (PROSE: Halflife)