| Summary: | 碩士 === 國立中正大學 === 數學研究所 === 103 === In this thesis we will introduce multiple zeta values.
These numbers have arisen in various contexts in geometry,
knot theory, mathematical physics, and arithmetical algebraic geometry.
As number theorists, we only concern about the relations on the multiple zeta values.
Here we especially study the linear relations over Q among the multiple zeta values.
We study multiple zeta values through a non-commutative algebra Q<x,y>.
Also, we will define the shuffle products on this algebra,
to get the finite double shuffle relations for multiple zeta values.
Next, we will take a number of derivations on some subalgebras of Q<x,y>
and the exponentiate them to obtain automorphisms,
in order to consider some identities of multiple zeta values,
such as Hoffman's relations and Ohno's relations.
Finally, we introduce the cyclic sum formula and Kawashima's relations.
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