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Multiple zeta function

In mathematics, the multiple zeta functions are generalizations of the Riemann zeta function, defined by

Integral structure and identities, Symmetric sums in terms of the zeta function & The sum and duality conjectures

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Integral structure and identities

IntegralsSymmetric groupFree monoidFreeVector space
8 related topics

Symmetric sums in terms of the zeta function

RealIsotropyEquivalence classesRelationCycle type
6 related topics

The sum and duality conjectures

ConjectureInvolutionStrictly increasingPartitions
4 related topics

Two parameters case

Harmonic numbersEulerOdd
3 related topics

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Overview

Definition

Integral structure and identities

Two parameters case

Euler reflection formula

Symmetric sums in terms of the zeta function

The sum and duality conjectures

Euler sum with all possible alternations of sign

Mordell–Tornheim zeta values

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Multiple zeta function

Nodes44
Edges43
Triples110
Avg. degree1.95
Density0.045455
Components1

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Multiple zeta function

Top relations

related to References · 78
Multiple zeta function → American Journal, American Mathematical Society, Analytic, Analytic Number Theory, Ankur, Apostol, Basu, Bonn, Bonner Math, Borwein, Bruno, Buhler, Chan, Cite, CiteSeerX, Comb, Diophantine Equations, Dirichlet, Duality, Electron
related to External links · 24
Multiple zeta function → Applications, Borwein, Burgos Gil, Fresán, Hoffman, ISBN, Javier, Jianqiang, Jonathan, José Ignacio, Lecture, Michael, Multiple, Multiple Polylogarithms, Multiple Zeta Functions, Number Theory, PDF, Series, Their Special Values, Vol
related to Definition · 4
Multiple zeta function → Euler, In, Multiple, When
related to Two parameters case · 4
Multiple zeta function → Euler, In, Multiple, MZV

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Important terminology

displaystyle zeta multiple sum cdots euler values sigma doi 10 mr sums function pi functions integers conjecture dots frac positive

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Multiple zeta functionrelated to DefinitionMultiple0.60section
Multiple zeta functionrelated to DefinitionWhen0.60section
Multiple zeta functionrelated to DefinitionIn0.60section
Multiple zeta functionrelated to DefinitionEuler0.60section
Multiple zeta functionrelated to External linksBorwein0.60section
Multiple zeta functionrelated to External linksJonathan0.60section
Multiple zeta functionrelated to External linksZudilin0.60section
Multiple zeta functionrelated to External linksWadim0.60section
Multiple zeta functionrelated to External linksLecture0.60section
Multiple zeta functionrelated to External linksHoffman0.60section
Multiple zeta functionrelated to External linksMichael0.60section
Multiple zeta functionrelated to External linksMultiple0.60section

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