4 problems

Quasi-admissibility and splitting conjecture. For all groups, quasi-admissibility of ${\mathcal O}$ is equivalent to the splitting of $\widetilde{M_\gamma}$.

Fourier-coefficient conjecture. The automorphic representation of $GL_2^{(r+1)}(\mathbb{A})$ generated by all the functions $f(g)$ is $\Theta_2^{(r+1)}$. The conjecture predicts th…

The global-integral conjecture. The integral $I(\varphi_\pi,s,f_s)$ has a meromorphic continuation to the full complex plane, and: (1) if $n<r+1$, it is identically zero for all…

For an odd-degree cover of the split odd orthogonal group $SO_{2r+1}$, consider the $p$-power contributions to the Whittaker coefficients of the minimal parabolic Eisenstein series…