Was Buddhism the dominant religion of India for one thousand years?

I read in a book by Amartya Sen 'The Argumentative Indian', (link ) that Buddhism was the dominant religion of India for about a 1000 years, and that foreigners referred to India as a Buddhist kingdom. Is it true? map from wikipedia shows that Buddhism was influential only in a small part of North-East India, and not at all in the southern or western part. Kindly provide online references, if possible.