For partially twisted multiple zeta-functions with polynomial denominators, the paper proves explicit formulas for the special values at non-positive integers and exhibits transcendental values in examples.
Essouabri, Singularit´ es de s´ eries de Dirichlet associ´ ees ` a des polynˆ omes de plusieurs variables et application en th´ eorie analytique des nombres, Ann
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Values at non-positive integers of partially twisted multiple zeta-functions II
For partially twisted multiple zeta-functions with polynomial denominators, the paper proves explicit formulas for the special values at non-positive integers and exhibits transcendental values in examples.