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

Hisashi Kojima, Hiroshi Sakata*

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)364-385
ページ数22
ジャーナルJournal of Number Theory
229
DOI
出版ステータスPublished - 2021 12

ASJC Scopus subject areas

  • 代数と数論

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