The book by Jacquet and
Robert Langlands on \operatorname{GL}(2) was an eclipsing event in the history of number theory. It presented a
representation theory of automorphic forms and their associated L−functions for the
general linear group \operatorname{GL}(2), establishing among other things the
Jacquet–Langlands correspondence which explains very precisely how automorphic forms for \operatorname{GL}(2) relate to those for
quaternion algebras. Equally important was the book by Godement and Jacquet, which defined, for the first time, the standard L-functions attached to automorphic representations of \operatorname{GL}(n), now called Godement–Jacquet L-functions, and proved their basic, oft-used analytic properties. His papers with
Joseph Shalika and the papers with
Ilya Piatetski-Shapiro and Shalika pertain to L-functions of pairs, called the Rankin-Selberg L-functions, attached to representations of \operatorname{GL}(n) and \operatorname{GL}(m), and the so-called converse theorem, which are crucial to our understanding of automorphic forms. A basic ingredient of this effort was an elaboration of properties of
Whittaker models and
functions, which Jacquet had made contributions to since his thesis. The papers with Shalika also established the uniqueness of isobaric decompositions of automorphic forms on \operatorname{GL}(n), thus providing evidence for certain conjectures of Langlands. In the mid-1980s, Jacquet forayed into a new territory in the field and created the
relative trace formula in representation theory, an important tool in modern number theory, which vastly generalizes the
Kuznetsov and
Petersson formulae from the classical setup. While the usual
Selberg trace formula, as well as its generalizations due to
James Arthur, consists in developing an expression for the integral of the kernel over the diagonal, the relative version integrates the kernel over other appropriate subgroups. ==Awards and honors==