On the Fourier coefficients of Hilbert–Maass wave forms of half integral weight over arbitrary algebraic number fields
✍ Scribed by Hisashi Kojima
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 457 KB
- Volume
- 107
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
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 C t from Hilbert-Maass wave forms f of half integral weight over algebraic number fields to Hilbert-Maass wave forms C t ð f Þ of integral weight over algebraic number fields. We shall determine explicitly the Fourier coefficients of C t ð f Þ 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 C t ð f Þ of f :