Nicht aus der Schweiz? Besuchen Sie lehmanns.de
The Theory of Zeta-Functions of Root Systems - Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

The Theory of Zeta-Functions of Root Systems (eBook)

eBook Download: PDF
2024 | 1st ed. 2023
IX, 414 Seiten
Springer Nature Singapore (Verlag)
978-981-99-0910-0 (ISBN)
Systemvoraussetzungen
128,39 inkl. MwSt
(CHF 125,40)
Der eBook-Verkauf erfolgt durch die Lehmanns Media GmbH (Berlin) zum Preis in Euro inkl. MwSt.
  • Download sofort lieferbar
  • Zahlungsarten anzeigen
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.

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.
Erscheint lt. Verlag 3.2.2024
Reihe/Serie Springer Monographs in Mathematics
Springer Monographs in Mathematics
Zusatzinfo IX, 414 p. 13 illus.
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Statistik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Functional relations • Mellin--Barnes Integral Formula • Multiple Zeta-Functions • root systems • Weyl groups
ISBN-10 981-99-0910-4 / 9819909104
ISBN-13 978-981-99-0910-0 / 9789819909100
Haben Sie eine Frage zum Produkt?
PDFPDF (Wasserzeichen)
Größe: 5,0 MB

DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasser­zeichen und ist damit für Sie persona­lisiert. Bei einer missbräuch­lichen Weiter­gabe des eBooks an Dritte ist eine Rück­ver­folgung an die Quelle möglich.

Dateiformat: PDF (Portable Document Format)
Mit einem festen Seiten­layout eignet sich die PDF besonders für Fach­bücher mit Spalten, Tabellen und Abbild­ungen. Eine PDF kann auf fast allen Geräten ange­zeigt werden, ist aber für kleine Displays (Smart­phone, eReader) nur einge­schränkt geeignet.

Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.

Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.

Mehr entdecken
aus dem Bereich