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


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

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


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