On a proof of Xu's Conjecture and depths of Galois descents

TL;DR

This paper provides an explicit formula confirming Xu's Conjecture on alternating double zeta values and discusses the limitations of motivic Galois descent criteria in determining the depth of Galois descents.

Contribution

It introduces an explicit formula for Xu's Conjecture and analyzes the constraints of existing motivic Galois descent methods.

Findings

Explicit formula confirming Xu's Conjecture

Limitations of Glanois' motivic Galois descent in depth specification

Insights into Galois descent depths

Abstract

We give an explicit formula proving Xu's Conjecture on alternating double zeta values. We also discuss the limitations of Glanois' motivic Galois descent criterion in this case, as it cannot specify the depth of the descent.