Author

Christopher Lutsko

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Preprint Sep 2026

Spherical density for real semisimple groups

Let $G$ be a connected semisimple real Lie group with finite center and let $(\Gamma_N)$ be a tower of cocompact lattices. We prove that the weak injective radius property implies the spherical density hypothesis with the same parameter. Together with the converse theorem of Golubev and Kamber, this gives an equivalenc...

Christopher Lutsko · 0 citations

Preprint Aug 2026

Improved sup-norm bounds for locally symmetric spaces

Let $X=G/K$ be a symmetric space of noncompact type, of dimension $n$ and rank $r$, and let $Y=\Gamma\backslash X$. Sarnak's local bound for an $L^2$-normalized spherical joint eigenfunction with regular tempered parameter of size $T$ is $\|\phi\|_\infty\ll T^{(n-r)/2}$. We prove $o(T^{(n-r)/2})$ locally uniformly on e...

Christopher Lutsko · 0 citations