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Transactions of the American Mathematical Society

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On the fundamental periods of Hilbert modular forms

Author: Ze-Li Dou
Journal: Trans. Amer. Math. Soc. 346 (1994), 147-158
MSC: Primary 11F67; Secondary 11F41
MathSciNet review: 1264144
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Abstract: The main purpose of this paper is to establish the existence of fundamental periods of primitive cusp forms of Hilbert modular type of several variables, as well as the relationship between those fundamental periods and the special values of the associated $ L$-functions. These results, together with some recent results of Shimura, give us the means of translating with ease results concerning periods of automorphic forms derived from various points of view. We also verify several conjectures of Shimura on the properties of such fundamental periods.

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Keywords: Periods, automorphic forms, modular forms, $ L$-functions, periods of modular forms, special values of $ L$-functions, cohomology of automorphic forms
Article copyright: © Copyright 1994 American Mathematical Society