2025/10/06 by Saito, Kyoji
#30C99 (primary) 33E05 (secondary) 33D05 (secondary) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.04558
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 Jacobi 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. The function appears also in the study of mathematical physics as the propagator on elliptic curves.