Photo by epicantus from unsplash
Abstract 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… Click to show full abstract
Abstract 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.
Keywords:
jacobi forms;
orders jacobi;
squarefree level;
eichler orders
Journal Title: Journal of Number Theory
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Journal of Number Theory
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!