Artin L-function on PGL3

Ming-Hsaun Kang; Wen-Chien Winnie Li

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arXiv · 1406.5277

Artin L-function on PGL3

Ming-Hsaun Kang·Wen-Chien Winnie Li

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Abstract

We study Artin $L$-functions on a finite $2$-dimensional complex $X_Γ$ arising from PGL$_3$ attached to finite-dimensional representations $ρ$ of its fundamental group. Some key properties, such as rationality, functional equation, and invariance under induction, of these functions are proved. Moreover, using a cohomological argument, we establish a connection between the Artin $L$- functions and the $L$-function of $ρ$, extending the identity on zeta functions of $X_Γ$ obtained in [KL,KLW].

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Ming-Hsaun Kang, Wen-Chien Winnie Li. 2014-06-20. Artin L-function on PGL3. https://arxiv.org/abs/1406.5277

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