The quasi-periods of the Weierstrass zeta-function

  • Mario Bonk

    University of California, Los Angeles, USA
The quasi-periods of the Weierstrass zeta-function cover

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Abstract

We study the ratio of the quasi-periods of the Weierstrass -function in dependence of the ratio of the gene­rators of the underlying rank-2 lattice. We will give an explicit geometric description of the map . As a consequence, we obtain an explanation of a theorem by Heins who showed that attains every value in the Riemann sphere infinitely often. Our main result is implicit in the classical literature, but it seems not to be very well known. Essentially, this is an expository paper. We hope that it is easily accessible and may serve as an introduction to these classical themes.

Cite this article

Mario Bonk, The quasi-periods of the Weierstrass zeta-function. Enseign. Math. (2024), published online first

DOI 10.4171/LEM/1085