On the modular forms of weight 1/2 over algebraic number fields

Hisashi Kojima, Hiroshi Sakata*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Serre and Stark succeeded in deciding a basis of the space of modular forms of weight 1/2 over the rational number field. Achimescu and Saha generalized their result to the case of modular forms of weight 1/2 over totally real algebraic number fields. Gove also solved this problem in the case of modular forms of weight 1/2 over imaginary quadratic fields. In this paper, we determine an explicit basis of the space of modular forms of weight 1/2, level c and character ψ over algebraic number fields. We prove our assertion using their arguments and Shimura's transformation formula of theta series over algebraic number fields.

Original languageEnglish
Pages (from-to)364-385
Number of pages22
JournalJournal of Number Theory
Volume229
DOIs
Publication statusPublished - 2021 Dec

Keywords

  • Automorphic forms on GL(2)
  • Forms of half-integer weight
  • Theta series

ASJC Scopus subject areas

  • Algebra and Number Theory

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