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Non-Archimedean L-functions of Siegel and Hilbert modular forms. (English) Zbl 0732.11026
Lecture Notes in Mathematics, 1471. Berlin etc.: Springer-Verlag. 157 p. DM 30.00 (1991).
Using the method of p-adic integration and of Rankin convolutions the author gives in great detail a construction of the p-adic L-functions attached to the standard zeta functions of Siegel modular forms and to the Rankin convolutions of Hilbert modular forms. In addition, a lot of background information is given on p-adic functions (p-adic measures, p- adic Mellin transforms etc.) and on Siegel- and Hilbert modular forms (theta series, Siegel-Eisenstein series, Hecke operators etc.); therefore the book should be accessible also to non-experts in the field.

##### MSC:
 11F85 $$p$$-adic theory, local fields 11S40 Zeta functions and $$L$$-functions 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11F66 Langlands $$L$$-functions; one variable Dirichlet series and functional equations 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.) 11F41 Automorphic forms on $$\mbox{GL}(2)$$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms