The contents of this book was created by the authors as a
simultaneous generalization of Witten zeta-functions,
Mordell–Tornheim multiple zeta-functions, and Euler–Zagier
multiple zeta-functions. Zeta-functions of root systems are defined
by certain multiple series, given in terms of root systems.
Therefore, they intrinsically have the action of associated Weyl
groups. The exposition begins with a brief introduction to
the theory of Lie algebras and root systems and then provides the
definition of zeta-functions of root systems, explicit examples
associated with various simple Lie algebras, meromorphic
continuation and recursive analytic structure described by Dynkin
diagrams, special values at integer points, functional relations,
and the background given by the action of Weyl groups. In
particular, an explicit form of Witten’s volume formula is
provided. It is shown that various relations among special values
of Euler–Zagier multiple zeta-functions—which usually are
called multiple zeta values (MZVs) and are quite important in
connection with Zagier’s conjecture—are just special cases of
various functional relations among zeta-functions of root systems.
The authors further provide other applications to the theory of
MZVs and also introduce generalizations with Dirichlet characters,
and with certain congruence conditions. The book concludes with a
brief description of other relevant topics.
General
| Imprint: |
Springer Verlag, Singapore
|
| Country of origin: |
Singapore |
| Series: |
Springer Monographs in Mathematics |
| Release date: |
November 2023 |
| Authors: |
Yasushi Komori
• Kohji Matsumoto
• Hirofumi Tsumura
|
| Dimensions: |
235 x 155mm (L x W) |
| Pages: |
426 |
| Edition: |
1st ed. 2023 |
| ISBN-13: |
978-981-9909-09-4 |
| Categories: |
Books
|
| LSN: |
981-9909-09-0 |
| Barcode: |
9789819909094 |
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