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Sup-norms of Maass forms on compact arithmetic surfaces in the level aspect

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Abhishek Saha
Queen Mary University of London
Thu, 2018-09-06 11:30 - 12:00
MPIM Lecture Hall

I will consider Maass forms transforming with respect to (unitary
characters of) unit groups of orders of an indefinite quaternion
division algebra over Q. I will assume that these Maass forms are
eigenfunctions of the Hecke operators at almost all primes not
dividing the level (or equivalently, that they generate an irreducible
automorphic representation). However, I will not make any assumptions
about the local components of these Maass forms at the primes dividing
the level (in particular they do not need to be newforms). I will
present an upper bound for the sup-norm of such Maass forms in the
level aspect that is valid for general orders and improves upon the
trivial bound. The key element in the proof is a uniform counting
result for points in quaternionic lattices.

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