A note on Poisson summation for GL(2)

Q: What type of study is this?

This is a Quantitative Study study.

Tian An Wong

doi:10.48550/arxiv.2510.02273

October 2, 2025Open Access

A note on Poisson summation for GL(2)

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Key Points

The analysis shows that the trivial representation's contribution to the trace formula can be effectively canceled.
Key findings indicate that applying a modified Poisson summation formula is crucial for understanding elliptic contributions.
The study employs an adelic perspective to re-examine previous methods in the context of GL(2).
These findings suggest significant implications for the broader understanding of representation theory and trace formulas.

Implication

Analytic number theory confirms cancellation of trivial representation in GL(2) trace formula, suggesting new adelic insights.

Abstract

Using analytic number theory techniques, Altuğ showed that the contribution of the trivial representation to the Arthur-Selberg trace formula for GL(2) over could be cancelled by applying a modified Poisson summation formula to the regular elliptic contribution. Drawing on recent works, we re-examine these methods from an adelic perspective.

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Cite This Study

Tian An Wong (2025) studied this question.

synapsesocial.com/papers/68e7d631bd66d359be6266d7 https://doi.org/10.48550/arxiv.2510.02273

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A note on Poisson summation for GL(2)

Key Points

Implication

Abstract

Discussion

Cite This Study

A note on Poisson summation for GL(2)

Key Points

Implication

Abstract

Discussion

Cite This Study

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