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Vector valued Siegel’s modular forms of degree two and the associated Andrianov \(L\)-functions. (English) Zbl 0517.10024


MSC:

11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
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References:

[1] A. N. Andrianov, Dirichlet series with Euler products in the theory of Siegel modular forms of genus 2, Trudy Mat. Inst. Steklov 112 (1971), 73-94. · Zbl 0224.10027
[2] A. N. Andrianov, Euler products corresponding to Siegel modular forms of genus 2, Uspekhi Mat. Nauk 29 (1974), 43-110. · Zbl 0304.10021
[3] M. Eichler, The basis problem for modular forms and the traces of the Hecke operators, Lect. Notes in Math. 320. Berlin-Heidelberg-New York: Springer 1973. · Zbl 0258.10013
[4] E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung I, Math. Ann. 114 (1937), 1-28. · Zbl 0015.40202
[5] H. Klingen, Zum Darstellungssatz fur Siegeische Modulformen, Math. Z. 102 (1967), 30-43. · Zbl 0155.40401
[6] T. Kubota, Über diskontinuierliche Gruppen Picardschen Typus und zugehörige Eisensteinsche Reihen, Nagoya Math. J. 32 (1968), 259-271. · Zbl 0159.31303
[7] R.P. Langlands, On the functional equations satisfied by Eisenstein series, Lect. Notes in Math. 544. Berlin-Heidelberg-New York: Springer 1976. · Zbl 0332.10018
[8] H. Maass, Die Primzahlen in der Theorie der Siegeischen Modulfuktionen, Math. Ann. 124 (1951), 87-122. · Zbl 0044.30901
[9] Séminaire H. Cartan, Ponctions automorphes, 1957-1958.
[10] G. Shimura, On modular correspondences for Sp(n,Z) and their congruence relations, Proc. Nat. Acad. U.S.A. 49 (1963), 824-828. · Zbl 0122.08803
[11] R. Tsushima, An explicit dimension formula for the spaces of generalized automorphic forms with respect to Sp(2,?), to appear in Proc. Japan Acad. · Zbl 0573.10016
[12] R. Tsushima, An explicit dimension formula for the spaces of generalized automorphic forms with respect to Sp(2,?), to appear. · Zbl 0573.10016
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