Work

An Arithmetic Defect beyond the Symplectic Trace Wall

Year: 2026

Type: preprint

Abstract: We study the fixed-distance range beyond the symplectic trace wall for quadratic L-functions over function fields. Using Wang's ratios theorem and a four-swap calculation, we identify an arithmetic Euler factor in the limiting second moment. For distance three, the first correction is 2/q^3 + O(q^-4), disproving universal post-wall saturation for all sufficiently large fixed odd prime powers. We also define the stable Euler coefficient for every fixed odd prime power and give a rigorous interval computation at q=3.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22208027

Authors: Liu, Ziyang, Wang, Yunxuan, Shi, Yao

Institutions: National University of Singapore, ETH Zurich, The Hong Kong University of Science and Technology (Guangzhou)

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204817268

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