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This is a Quantitative Study study.

October 12, 2025Open Access

The trace formula of GL(3)

Key Points

The study shows that the divergent terms of the trace formula of GL(3) are equal, contributing to the Langlands program.
Explicit formulas for ramified orbits are provided, demonstrating their expression as limits of distributions of unramified orbits.
The truncation operator is applied to ensure convergence on both sides of the trace formula for GL(3).
Analysis focuses on the geometric side of GL(3), providing insights into the relationship between ramified and unramified orbits.

Abstract

Trace formula is an important method to study the Langlands program. In this paper, we will give the explicit coarse trace formula of (3). In general case, Arthur applies the truncation operator on the two sides of trace formula such that they are convergent. In our case, we will prove that the divergent terms of the two sides of the trace formula of (3) are equal. We also obtain the explicit formula for ramified orbits of the geometric side of (3), and show it can be expressed as a limit of distributions of the unramified orbits.

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Cite this study

Xinghua et al. (Fri,) studied this question.

synapsesocial.com/papers/68ec384042a190b2c3519833 — DOI: https://doi.org/10.48550/arxiv.2509.05312

Authors

Cui Xinghua

Wang Haoyang

Peng Zhifeng

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The trace formula of GL(3)

Key Points

Abstract

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Discussion

Cite this study

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion