Year: 2025
Type: preprint
Abstract: We prove that $\mathsf{OT}_η(T)\ll T\log^2 T$ unconditionally via a band-limited test scheme with Fejér averaging. The approach normalizes $\|\widehat f\|_1=Θ(T^{-1})$ to ensure $\|h\|_1\asymp T$ and $\|\widehat h\|_1\ll 1$, and applies an $L^1$-controlled smoothed explicit formula to bound the error terms. As a result, the prime--zero optimal transport distance admits the baseline $T\log^2 T$ upper bound without additional assumptions.
Source: arXiv (Cornell University)
Author: Yang, Zhejun
Institution: The University of Sydney
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416065769
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