On Whittaker coefficients of some metaplectic forms
The authors construct from any two holomorphic Hecke eigenforms of square-free level \(N\) satisfying certain additional conditions an automorphic form on the double cover of \(\text{GSp}(4)\) such that some of its `Fourier coefficients' are products of the Fourier coefficients of the original forms at certain integers. (It has not been ruled out that the product is always zero.) The construction of the form is carried out by a series of theta-lifts; first of all the original forms are represented as lifts from a quaternion algebra. Then the pair of forms on the quaternion algebra is lifted to a (non-metaplectic) form on the symplectic group. Finally this is lifted to the double cover of the symplectic group using the exceptional isomorphism \({\mathfrak {sp}}(4) \cong {\mathfrak o} (5)\). That a construction which such properties should be possible was conjectured in 1989 by Bump, Friedberg and Hoffstein.
scientific article; zbMATH DE number 755396
scientific article