Gotham font here refers to the font used in the logo of Gotham, which is an American crime television series developed by Bruno Heller, based on characters appearing in and published by DC Comics in their Batman franchise.
The font used for the logo the Gotham TV show is probably Arno regular. Designed by Robert Slimbach and named after the river that runs through Florence, the center of the Italian Renaissance, Arno is an old style serif typeface that draws its inspiration from 15th and 16th century early humanistic typefaces and is designed in the tradition of early book types such as Venetian and Aldine. You can read more about it here.
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