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

2025/08/04 by Charlton, Steven
#11M32 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.02648

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.

Citations

• Evaluations of nonlinear Euler sums of weight ten
• Periods of the motivic fundamental groupoid of \boldsymbolℙ¹ \diagdown \lbrace 0, μ_N, ∞ \rbrace
• Depth-graded motivic multiple zeta values
• Multiple polylogarithms and mixed Tate motives
• On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory

Related

• Motivic multiple zeta values reletive to μ₂
• The depth structure of motivic multiple zeta values
• Multiple zeta values with varying constant fields
• Difference Galois Theory For The "Applied" Mathematician
• On a conjecture of Zhao related to standard relations among cyclotomic multiple zeta values