COUNTING ZEROS IN QUATERNION ALGEBRAS USING JACOBI FORMS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.371, sa.9, ss.6487-6509, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 371 Sayı: 9
- Basım Tarihi: 2019
- Doi Numarası: 10.1090/tran/7575
- Dergi Adı: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.6487-6509
- İstanbul Üniversitesi Adresli: Evet
Özet
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-r(2)). 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 Gamma(0)(N) and for the action of Hecke operators on Jacobi theta series associated to maximal orders of definite quaternion algebras.