Functional equations for Weng's zeta functions for $(G,P)/\mathbb{Q}$

TL;DR

This paper proves that Weng's zeta functions linked to semisimple algebraic groups over the rationals and their maximal parabolic subgroups satisfy certain functional equations, extending understanding of their symmetry properties.

Contribution

It establishes the functional equations for Weng's zeta functions associated with arbitrary semisimple groups over ield and their maximal parabolic subgroups, a previously unproven property.

Findings

Weng's zeta functions satisfy functional equations

The results apply to arbitrary semisimple algebraic groups over ield

The functional equations relate values at s and 1-s

Abstract

It is shown that Weng's zeta functions associated with arbitrary semisimple algebraic groups defined over the rational number field and their maximal parabolic subgroups satisfy the functional equations.