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arXiv · 2002.08906

On the Mirabolic Trace Formula for $\mathfrak{gl}(n)$

Shuyang Cheng
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Abstract

In this paper, a Chaudouard type trace formula is established for the Lie algebra $\mathfrak{gl}(n)$, by integrating the Lie algebra analogue of the Selberg kernel function against a mirabolic Eisenstein series on $\mathrm{GL}(n)$. The result is a combination of zeta functions $ζ_E(s)$ of extensions over the base field $F$ of degree $[E:F]\leq n$.

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Shuyang Cheng. 2020-11-20. On the Mirabolic Trace Formula for $\mathfrak{gl}(n)$. https://arxiv.org/abs/2002.08906

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