Reference: Mœglin, C.; Waldspurger, J.-L.: Le spectre residuel de GL(n)

On GL($n$), the result of Waldspurger shows that if an automorphic representation $\pi$ is non-cuspidal and in the discrete spectrum, then there is $d|n$ and an automorphic representation $\tau$ on GL($d$) such that $\pi$ is the residue of the Eisenstein seires $E(*,\tau,n/d)$ induced from a direct sum of ($n/d$) copies of $\tau$.

I am wondering what these $\pi$ look like? What's their $L$-functions (in terms of $\tau$)?

The $L$-function of $E(*,\tau,n/d)$ may look like $L(s,\tau)^{n/d}$? But how about its residue?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.