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Orthogonality relation between GL(3) coefficients and additive characters with linear and non-linear phases
Abstract
We study the distribution and oscillatory properties of prime-supported Fourier coefficients attached to a Hecke--Maass form for SL(3, ℤ) twisted by additive characters. For linear phases involving irrationals of finite type, we construct an automorphic variant of Vaughan's identity and exploit bilinear cancellation to obtain an unconditional power-saving estimate. For non-linear phases e(αnθ) with 0 < θ< 1, we refine the Type~II bilinear forms via Weyl differencing and modern exponent pair methods. Combined with the analysis of untwisted GL(3) sums, this framework breaks the 2/3-barrier of Jiang and Lü and widens the admissible range of non-trivial cancellation.
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BibTeX
@misc{venkatasubbareddy2026orthogonality,
title = {{Orthogonality relation between $GL(3)$ coefficients and additive characters with linear and non-linear phases}},
author = {K. Venkatasubbareddy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18928},
eprint = {2610.18928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18928},
}
RIS
TY - UNPB
TI - Orthogonality relation between GL(3) coefficients and additive characters with linear and non-linear phases
AU - K. Venkatasubbareddy
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18928
UR - https://arxiv.org/abs/2610.18928
AB - We study the distribution and oscillatory properties of prime-supported Fourier coefficients attached to a Hecke--Maass form for SL(3, ℤ) twisted by additive characters. For linear phases involving irrationals of finite type, we construct an automorphic variant of Vaughan's identity and exploit bilinear cancellation to obtain an unconditional power-saving estimate. For non-linear phases e(αn^θ) with 0 < θ< 1, we refine the Type~II bilinear forms via Weyl differencing and modern exponent pair methods. Combined with the analysis of untwisted GL(3) sums, this framework breaks the 2/3-barrier of Jiang and Lü and widens the admissible range of non-trivial cancellation.
ER -