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 -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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1264144-9

Keywords:
Periods,
automorphic forms,
modular forms,
-functions,
periods of modular forms,
special values of -functions,
cohomology of automorphic forms

Article copyright:
© Copyright 1994
American Mathematical Society