- COUNTING ZEROS IN QUATERNION ALGEBRAS USING JACOBI FORMS
- 点击次数：
- 影响因子：1.318
- 所属单位：数学科学学院
- 发表刊物：TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- 刊物所在地：201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
- 项目来源：National Natural Science Foundation of China (Grant No. 11271283)
- 关键字：Jacobi forms, arithmetic of quaternion algebras
- 摘要：We use the theory of Jacobi forms to study the number of elements in a maximal order of a definite quaternion algebra over the field of rational numbers whose characteristic polynomial equals a given polynomial. A certain weighted average of such numbers equals (up to some trivial factors) the Hurwitz class number H(4n−r2). As a consequence we obtain new proofs for Eichler’s trace formula and for formulas for the class and type number of definite quaternion algebras. As a secondary result we derive explicit formulas for Jacobi Eisenstein series of weight 2 on Γ0(N) and for the action of Hecke operators on Jacobi theta series associated to maximal orders of definite quaternion algebras.
- 合写作者：周海港
- 论文类型：期刊论文
- 卷号：371
- 期号：9
- 页面范围：6487-6509
- ISSN号：0002-9947
- 是否译文：否
- 发表时间：2019-01-01
- 收录刊物：SCOPUS、CNKI、WOS
