We prove Ibukiyama’s conjectures on Siegel modular forms of half-integral weight and degree 2 by using Arthur’s multiplicity formula the split odd special orthogonal group $${\text {SO}}_5$$ Gan–Ichino’s metaplectic {Mp}}_4$$ . In proof, representation theory Jacobi groups also plays an important role.

We construct liftings of cuspidal automorphic forms from the metaplectic group S̃L2 to GSpin(1, 4) using the Maaß Converse Theorem. In order to prove the non-vanishing of the lift we derive Waldspurger’s formula for Fourier coefficients of half integer weight Maaß forms. We analyze the automorphic representation of the adelic spin group obtained from the lift and show that it is CAP to the Saito...

The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions [13] which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms of metaplectic Eisenstein series on GL(2). The converse theorem we prove will apply to a very general family of double Dirichlet series which...

Abstract. We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslovtype indices; these indices intervene in a crucial way in Gutzwiller’s formula of semiclassical mechanics, and are simply related to a...

The subject of this thesis is the theory of nonholomorphic modular forms of non-integral weight, and its applications to arithmetical functions involving Dedekind sums and Kloosterman sums. As was discovered by Andre Weil, automorphic forms of non-integral weight correspond to invariant funtions on Metaplectic groups. We thus give an explicit description of Meptaplectic groups corresponding to ...

We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However they are not Eulerian and the standard methods to compute them in the reductive case do not apply to covers. For “cominuscule” maximal parabolics, we give an e...