2 problems

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…