Work

On the representability of Hilbert cusp forms by theta series

Year: 2025

Type: article

Abstract: Using trace formulas for Hecke operators, Eichler first provided a positive solution about basis problems of elliptic cusp forms by quadratic forms. J-L. Waldspurger established that elliptic cusp forms of arbitrary level are spanned by theta series by means of different and interesting ideas and methods. This result is given by Zagier’s analytic theorems, the Siegel main theorem of quadratic forms and the theory of Hecke operators. We intend to generalize Waldspurger’s results and determine theta series which span the space of Hilbert new forms over arbitrary totally real algebraic number fields following Waldspurger’s methods.

Source: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

DOI: 10.1007/s12188-025-00290-y

Authors: Hisashi Kojima, Hiroshi Sakata

Institutions: Saitama University, Waseda University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Waseda University, Japan Society for the Promotion of Science