Mixed motives and linear forms in the Catalan constant

2025/10/23 by Eskandari, Payman, Murty, Kumar, Nemoto, Yusuke
#11G99 #11M06 #14F42 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.20648

Abstract

We first give a geometric construction of a 2-dimensional mixed motive over ℚ with the Catalan constant G=1-1/3²+1/5²-1/7²+⋯ as a period. We then use this motive to obtain a supply of linear forms in 1 and G. We also explicitly compute the coefficients of 1 and G in these linear forms.

Citations

• A construction of the polylogarithm motive
• Irrationality proofs for zeta values, moduli spaces and dinner parties
• Groupes fondamentaux motiviques de Tate mixte

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