"Archer had seen 'Silver Linings Playbook' and instantly recognised Kher. They spoke about both Indian cinema and food," said a statement.
Archer liked the title of Anupam's book "The Best Thing About You Is You". Archer signed it for him and asked him to keep in touch.
The five-day literature festival concluded Saturday.
Directed by David O. Russell, "Silver Linings Playbook" also features Bradley Cooper and Jennifer Lawrence.
Anupam, 58, played Dr. Patel in the film.
On home turf, the actor is looking forward to the release of "Chashme Baddoor" and "Yamla Pagla Deewana 2".