5
$\begingroup$

The spectrum of the Laplacian on $L^2$ of a Hilbert modular surface decomposes into a discrete part and a continuous part $[1/4,\infty)$. The continuous part contains eigenvalues $\geq 1/4$.

I would like to know if the eigenfunctions of such eigenvalues lie also in $L^p$ for some $p>2$. If so, why?

$\endgroup$
1
  • 4
    $\begingroup$ For dimension one the answer is yes, as all those eigenfunctions are cusp forms which decay exponentially at the cusps. I think a similar argument should settle the case of Hilbert forms as well. $\endgroup$
    – user1688
    Jan 11, 2017 at 11:37

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.