Abstract:We establish sharp bounds for the second moment of symmetric-square L-functions attached to Hecke Maass cusp forms
$u_j$
with spectral parameter
$t_j$
, where the second moment is a sum over
$t_j$
in a short interval. At the central point
$s=1/2$
of the L-function, our interval is smaller than previous known results. More specifically, for
$\left \lvert t_j\right \rvert $
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We improve on the spectral large sieve inequality for symmetric-squares. We also prove a lower bound showing that the most optimistic upper bound is not true for this family.
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