REVIEW 1 cited by
Theta functions, fourth moments of eigenforms, and the sup-norm problem III
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
In the prequel, a sharp bound in the level aspect on the fourth moment of Hecke--Maa{\ss} forms with an inexplicit (in fact exponential) dependency on the eigenvalue was given. In this paper, we develop further the framework of explicit theta test functions in order to capture the eigenvalue more precisely. We use this to reduce a sharp hybrid fourth moment bound to an intricate counting problem. Unconditionally, we give a hybrid bound, which is sharp in the level aspect and with a slightly larger than convex dependency on the eigenvalue.
Forward citations
Cited by 1 Pith paper
-
Spectral fourth moments of Hecke--Maa{\ss} cusp forms
For Heegner points, the spectral fourth moment of Hecke–Maass cusp forms in a dyadic interval is O(T^{2+ε}), matching the Lindelöf-on-average prediction.
Discussion (0). Continue with ORCID to comment.