On Shimura's correspondence
The authors make an important contribution to the theory of the generalized Shimura correspondence for GL(2) which was proved using the Selberg trace formula by Y. Z. Flicker. They show that if \(\phi\) is an automorphic form on an n-fold cover of GL(2) over a number field then this corresponds to an automorphic form \(\phi\) on GL(2). To \(\phi\) one can associate an L-function. The crux of the author's method is that they show that this L-function can also be represented essentially as a global integral of a type introduced by H. Jacquet, and that the analytic properties of the L-function can be deduced from this representation. The integral involves the metaplectic theta function on the n-fold cover of GL(n). Central to this approach is a very interesting calculation at the unramified places. The results are almost, but not quite enough to give an ``L-function'' proof of the Shimura correspondence in the case of GL(2).
generalized Shimura correspondence for GL(2)
scientific article; zbMATH DE number 4025512
scientific article