On the Fourier coefficients of Hilbert-Maass wave forms of half integral weight over arbitrary algebraic number fields |
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Authors: | Hisashi Kojima |
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Institution: | Department of Mathematics, Faculty of Education, Iwate University, Morioka 020-8550, Japan |
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Abstract: | The purpose of this paper is to derive a generalization of Shimura's results concerning Fourier coefficients of Hilbert modular forms of half integral weight over total real number fields in the case of Hilbert-Maass wave forms over algebraic number fields by following the Shimura's method. Employing theta functions, we shall construct the Shimura correspondence Ψτ from Hilbert-Maass wave forms f of half integral weight over algebraic number fields to Hilbert-Maass wave forms of integral weight over algebraic number fields. We shall determine explicitly the Fourier coefficients of in terms of these f. Moreover, under some assumptions about f concerning the multiplicity one theorem with respect to Hecke operators, we shall establish an explicit connection between the square of Fourier coefficients of f and the central value of quadratic twisted L-series associated with the image of f. |
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Keywords: | 11F37 11F30 |
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