Evaluations of multiple Dirichlet $L$-values via symmetric functions

Abstract

We explicitly evaluate a special type of multiple Dirichlet $L$-values at positive integers in two different ways: One approach involves using symmetric functions, while the other involves using a generating function of the values. Equating these two expressions, we derive several summation formulae involving the Bernoulli and Euler numbers. Moreover, values at non-positive integers, called central limit values, are also studied.

18 pages

References in corpus (7)

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Cited by in corpus (5)

• The Bowman-Bradley theorem for multiple zeta-star values
• A study on multiple zeta values from the viewpoint of zeta-functions of root systems
• On some combinations of multiple zeta-star values
• On Schur multiple zeta functions: A combinatoric generalization of multiple zeta functions
• Infinite products involving Dirichlet characters and cyclotomic polynomials