Veltman, Niek (2022) Linear Relations for Multiple Zeta Values. Bachelor's Thesis, Mathematics.
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Abstract
To look into algebraic relations for zeta values, it is useful to introduce multiple zeta values. Multiple zeta values can both be represented by a series and by an integral. From this integral representation, we derive the Duality theorem, which gives equalities between multiple zeta values. Furthermore, it is possible to compare the multiplication of two multiple zeta values given by the different representations. By doing so, the finite double shuffle relation occurs. To generalize this relation, we introduce the so-called stuffle and shuffle product on a non-commutative polynomial algebra. Furthermore, we explore other linear relations for multiple zeta values. One of them is the integral series identity, which is conjectured to imply all other linear relations for multiple zeta values. We derive Hoffman's relation and the restricted sum formula from this identity to support this conjecture. Finally, we look into the dimension and basis for the spaces spanned by multiple zeta values for a fixed weight. The dimension and basis for these spaces are conjectured by Zagier's conjecture and Hoffman's conjecture, respectively. We work out some examples of Brown's theorem, which partially proves Hoffman's conjecture.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Ludtke, M.W. and Lorscheid, O. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 19 Jul 2022 07:30 |
| Last Modified: | 19 Jul 2022 07:30 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27967 |
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