A1 Refereed original research article in a scientific journal
Ω-results for exponential sums related to Maass cusp forms for SL3(ℤ)
Authors: Jääsaari, Jesse
Publisher: Cambridge University Press (CUP)
Publication year: 2026
Journal: Mathematical Proceedings of the Cambridge Philosophical Society
ISSN: 0305-0041
eISSN: 1469-8064
DOI: https://doi.org/10.1017/S0305004125101813
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1017/S0305004125101813
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/508164196
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
We obtain Ω -results for linear exponential sums with rational additive twists of small prime denominators weighted by Hecke eigenvalues of Maass cusp forms for the group SL3(ℤ). In particular, our Ω -results match the expected conjectural upper bounds when the denominator of the twist is sufficiently small compared to the length of the sum. Non-trivial Ω-results for sums over short segments are also obtained. Along the way we produce lower bounds for mean squares of the exponential sums in question and also improve the best known upper bound for these sums in some ranges of parameters.
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Funding information in the publication:
During the research the author was supported by the Finnish Cultural Foundation, by the Emil Aaltonen Foundation, and by the Engineering and Physical Sciences Research Council [grant number EP/T028343/1].
