TY - JOUR A1 - Guo, Li A1 - Paycha, Sylvie A1 - Zhang, Bin T1 - Conical zeta values and their double subdivision relations JF - Advances in mathematics N2 - We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values. In order to achieve the closed cone subdivision relation, we also interpret linear relations among fractions as subdivisions of decorated closed cones. As a generalization of the double shuffle relation of multiple zeta values, we give the double subdivision relation of conical zeta values and formulate the extended double subdivision relation conjecture for conical zeta values. KW - Convex cones KW - Conical zeta values KW - Smooth cones KW - Decorated cones KW - Subdivisions KW - Multiple zeta values KW - Shuffles KW - Quasi-shuffles KW - Fractions with linear poles KW - Shintani zeta values Y1 - 2014 U6 - https://doi.org/10.1016/j.aim.2013.10.022 SN - 0001-8708 SN - 1090-2082 VL - 252 SP - 343 EP - 381 PB - Elsevier CY - San Diego ER -