Eichler orders and Jacobi forms of squarefree level

Autor:	Yan-Bin Li, Nils-Peter Skoruppa, Haigang Zhou
Rok vydání:	2022
Předmět:	Pure mathematics Rational number Class (set theory) Algebra and Number Theory Series (mathematics) Quaternion algebra Mathematics::Number Theory Field (mathematics) Square-free integer symbols.namesake Eisenstein series symbols Fourier series Mathematics
Zdroj:	Journal of Number Theory. 236:349-387
ISSN:	0022-314X
Popis:	For all Eichler orders with a same squarefree level in a definite quaternion algebra over the field of rational numbers, we prove that a weighted sum of Jacobi theta series associated to these orders is a Jacobi Eisenstein series. Multiply the Fourier coefficients of the latter by a power of 2 to get our modified Hurwitz class numbers. As its corollaries, the modified Hurwitz class numbers can be used to calculate the traces of Brandt matrices and the type number of the Eichler orders.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::97d06b1cc7baa6f6295dc2905e861d7f https://doi.org/10.1016/j.jnt.2021.07.025 Zobrazit plný text záznamu Full Text from ScienceDirect