2024/05/27 by Jesse Jääsaari, Jääsaari, Jesse
Mathematics · #11F30 #11L07 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2405.17340
openalex publication_date 2024/05/27 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28
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(\mathbb 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.