Joint IAS/PU Groups and Dynamics Seminar
$L^4$-Norms of Automorphic Forms in the Depth Aspect
A classical problem in harmonic analysis is to understand how the mass of Laplace eigenfunctions distributes as their parameters tend to infinity. In this talk, I will consider this problem on arithmetic hyperbolic surfaces obtained as quotients of the upper half plane by congruence subgroups of $SL_2(Z)$. I will focus on the depth aspect, where the level of the surface grows through powers of a fixed prime. More precisely, let f be an $L^2$-normalized newform for $GL(2)$ of level $p^n$, with p a fixed odd prime, and n tending to infinity. Assuming that f has trivial central character and bounded spectral parameters, I will discuss the optimal bound for its $L^4$-norm and the analogies with the spectral aspect.
Date & Time
November 10, 2026 | 4:30pm – 5:30pm
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11/10/2026 16:30
11/10/2026 17:30
Joint IAS/PU Groups and Dynamics Seminar
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Topic: $L^4$-Norms of Automorphic Forms in the Depth Aspect
Speakers: Marius Fischer, Aarhus University
More: https://www.ias.edu/math/events/joint-iaspu-groups-and-dynamics-seminar-60
A classical problem in harmonic analysis is to understand how the mass
of Laplace eigenfunctions distributes as their parameters tend to
infinity. In this talk, I will consider this problem on arithmetic
hyperbolic surfaces obtained as quotients of the upper half plane by
congruence subgroups of $SL_2(Z)$. I will focus on the depth aspect,
where the level of the surface grows through powers of a fixed prime.
More precisely, let f be an $L^2$-normalized newform for $GL(2)$ of
level $p^n$, with p a fixed odd prime, and n tending to infinity.
Assuming that f has trivial central character and bounded spectral
parameters, I will discuss the optimal bound for its $L^4$-norm and
the analogies with the spectral aspect.
Simonyi 101
a7a99c3d46944b65a08073518d638c23
Location
Simonyi 101Speakers
Marius Fischer, Aarhus University