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Subconvexity bounds on the critical line are proved for general Epstein zeta-functions of 
$k$-ary quadratic forms. This is related to sup-norm bounds for unitary Eisenstein series on 
$\text{GL}(k)$ associated with the maximal parabolic of type 
$(k-1,1)$, and the exact sup-norm exponent is determined to be 
$(k-2)/8$ for 
$k\geqslant 4$. In particular, if 
$k$ is odd, this exponent is not in 
$\frac{1}{4}\mathbb{Z}$, which is relevant in the context of Sarnak’s purity conjecture and shows that it can in general not directly be generalized to Eisenstein series.
We prove upper bounds for Hecke–Laplace eigenfunctions on certain Riemannian manifolds 
$X$ of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are 
$d$-fold products of 
$2$-spheres or 
$3$-spheres, realized as adelic quotients of quaternion algebras over totally real number fields. In the volume aspect we prove a (‘Weyl-type’) saving of 
$\mathrm{vol} \hspace{0.167em} (X)^{- 1/ 6+ \varepsilon } $.
