Bergman space zero sets, modular forms, von Neumann algebras and ordered groups
Vaughan F. R. Jones
Vanderbilt University, Nashville, USA
![Bergman space zero sets, modular forms, von Neumann algebras and ordered groups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-lem-volume-69-issue-1.png&w=3840&q=90)
Abstract
will denote the weighted Bergman space. Given a subset of the open unit disc we define to be the infimum of having as its zero set. By classical results on Hardy space there are sets for which . Using von Neumann dimension techniques and cusp forms we give examples of where . By using a left order on certain Fuchsian groups we are able to calculate exactly if is the orbit of a Fuchsian group. This technique also allows us to derive in a new way well known results on zeros of cusp forms and indeed calculate the whole algebra of modular forms for .
Cite this article
Vaughan F. R. Jones, Bergman space zero sets, modular forms, von Neumann algebras and ordered groups. Enseign. Math. 69 (2023), no. 1/2, pp. 5–36
DOI 10.4171/LEM/1045