1 results
On the Kohnen plus space for Hilbert modular forms of half-integral weight I
- Part of
-
- Journal:
- Compositio Mathematica / Volume 149 / Issue 12 / December 2013
- Published online by Cambridge University Press:
- 06 September 2013, pp. 1963-2010
- Print publication:
- December 2013
-
- Article
-
- You have access
- Export citation
-
In this paper, we construct a generalization of the Kohnen plus space for Hilbert modular forms of half-integral weight. The Kohnen plus space can be characterized by the eigenspace of a certain Hecke operator. It can be also characterized by the behavior of the Fourier coefficients. For example, in the parallel weight case, a modular form of weight
$\kappa + (1/ 2)$ with 
$\xi \mathrm{th} $ Fourier coefficient 
$c(\xi )$ belongs to the Kohnen plus space if and only if 
$c(\xi )= 0$ unless 
$\mathop{(- 1)}\nolimits ^{\kappa } \xi $ is congruent to a square modulo 
$4$. The Kohnen subspace is isomorphic to a certain space of Jacobi forms. We also prove a generalization of the Kohnen–Zagier formula.
