Joint work with Deny Item 83: On the ratio of two negative definite functions. By Arne Beurling and Jacques Deny. Typed manuscript intended for publication, pp. 1–27 (pdf). Preceded by a letter from Deny of Jan 6, 1964. pp. 1 + Deny’s comment to paper, 1 page. The main results of this paper appeared in Kahane’s Bourbaki seminar talk, but in the special case when G = .