Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 1

Special Issue in honor of Don Zagier

Guest editors: Benedict H. Gross, Ken Ono, and Fernando Rodriguez Villegas

Span of restriction of Hilbert theta functions

Pages: 61 – 83

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n1.a4

Authors

Gabriele Bogo (Fachbereich Mathematik, Technische Universität Darmstadt, Germany)

Yingkun Li (Fachbereich Mathematik, Technische Universität Darmstadt, Germany)

Abstract

In this paper, we study the diagonal restrictions of certain Hilbert theta series for a totally real field $F$, and prove that they span the corresponding space of elliptic modular forms when the $F$ is quadratic or cubic. Furthermore, we give evidence of this phenomenon when $F$ is quartic, quintic and sextic.

Received 8 April 2022

Received revised 28 June 2022

Accepted 21 July 2022

Published 3 April 2023