On the Kohnen plus space for Hilbert modular forms of half-integral weight I.
In: Compositio Mathematica, Jg. 149 (2013-12-01), Heft 12, S. 1963-2010
Online
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Zugriff:
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. [ABSTRACT FROM PUBLISHER]
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On the Kohnen plus space for Hilbert modular forms of half-integral weight I.
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Autor/in / Beteiligte Person: | Hiraga, Kaoru ; Ikeda, Tamotsu |
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Zeitschrift: | Compositio Mathematica, Jg. 149 (2013-12-01), Heft 12, S. 1963-2010 |
Veröffentlichung: | 2013 |
Medientyp: | academicJournal |
ISSN: | 0010-437X (print) |
DOI: | 10.1112/S0010437X13007276 |
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