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Abstract

We illustrate a rank 1 model of virtual period maps and their associated winding quotient, where the winding quotient is a new phenomenon appeared in a recent study of virtual period maps and it requires a reformulation of the classical inversion problem for the period maps. We answer to the new inversion problem by introducing the q-multiplicatively periodic function, whose pull-back to the winding covering space is the Weierstrass p-function up to a correction by Eisenstein series E2, and which was used in recent mathematical physics.