Mixed motives and linear forms in the Catalan constant

Payman Eskandari, Kumar Murty, Yusuke Nemoto

We first give a geometric construction of a 2-dimensional mixed motive over $\mathbb{Q}$ with the Catalan constant $\mathbf{G}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use…