Multiple zeta values (MZVs) are defined by convergent series $$\zeta(n_1,n_2,...,n_r)=\sum_{00,n_r>1.$$
The theory of MZVs plays an important role in the theory of mixed Tate motives, Feynman diagram, knot theory, etc.
In (Kaneko, Tasaka, 2014), Kaneko and Tasaka studied the sum odd version double zeta values (the convergent series are sum over odd numbers) . They found an interesting connection between sum odd double zeta values and cusp forms of \gamma_0(2). Further more, they proposed three conjectures about the relations between sum odd double zeta values and classical multiple zeta values.
In this talk I will first give the definition of motivic multiple zeta values. I will show how to get a short exact sequence which involved motivic sum odd double zeta values and period polynomial of \gamma_0(2) by using the theory of mixed Tate motives. A basis for motivic double zeta values and a basis for motivic triple zeta values will be given. As an application of our main results, we prove Kaneko and Tasaka’s three conjectures.