Petersson inner products of weight-one modular forms

Viazovska, Maryna

doi:10.1515/crelle-2016-0042

アイテム詳細

登録内容を編集ファイル形式で保存

一時保存へ追加

タグ情報を表示リリース履歴を表示詳細要約

公開

学術論文

Petersson inner products of weight-one modular forms

MPS-Authors

/persons/resource/persons236399

Viazovska, Maryna
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1515/crelle-2016-0042
(出版社版)

https://doi.org/10.48550/arXiv.1211.4715
(プレプリント)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

フルテキスト (公開)

公開されているフルテキストはありません

付随資料 (公開)

There is no public supplementary material available

引用

Viazovska, M. (2019). Petersson inner products of weight-one modular forms. Journal für die Reine und Angewandte Mathematik, 749, 133-159. doi:10.1515/crelle-2016-0042.

引用: https://hdl.handle.net/21.11116/0000-0004-F859-1

要旨

n this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that these Petersson products posses remarkable arithmetic properties. Namely, such a Petersson product
is equal to the logarithm of a certain algebraic number lying in a ring class field associated
to the binary quadratic form. A similar result was obtained independently using a different
method by W. Duke and Y. Li [5]. The main result of this paper is an explicit factorization
formula for the algebraic number obtained by exponentiating a Petersson product.