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 ...
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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.
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New. Contains: Illustrations, black & white. Springer Monographs in Mathematics . IX, 414 p. 13 illus. Intended for professional and scholarly audience.
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New. Contains: Illustrations, black & white. Springer Monographs in Mathematics . IX, 414 p. 13 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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New. Print on demand Contains: Illustrations, black & white. Springer Monographs in Mathematics . IX, 414 p. 13 illus. Intended for professional and scholarly audience.
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New. Contains: Illustrations, black & white. Springer Monographs in Mathematics . IX, 414 p. 13 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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Fine. Contains: Illustrations, black & white. Springer Monographs in Mathematics . IX, 414 p. 13 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
