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We consider a generalization of elliptic multiple zeta values, which we calltwisted elliptic multiple zeta values. These arise as iterated integrals on anelliptic curve from which a rational lattice has been removed. At the cusp,twisted elliptic multiple zeta values are shown to degenerate to cyclotomicmultiple zeta values in the same way as elliptic multiple zeta valuesdegenerate to classical multiple zeta values. We investigate properties oftwisted elliptic multiple zeta values and consider them in the context of thenon-planar part of the four-point one-loop open-string amplitude.

Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes