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On the poles of Andrianov L-functions. (English) Zbl 0465.10021


MSC:

11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F27 Theta series; Weil representation; theta correspondences
11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
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References:

[1] Andrianov, A.N.: Dirichlet series with Euler product in the theory of Siegel modular forms of genus 2. Trudy Mat. Inst. Steklov.112, 73–94 (1971) · Zbl 0224.10027
[2] Andrianov, A.N.: Euler products corresponding to Siegel modular forms of genus 2. Uspehi Mat Nauk29, 43–110 (1974) · Zbl 0304.10021
[3] Andrianov, A.N.: Siegel modular forms and zeta-functions. Trud. Mat. Inst. Steklov132, 132–136 (1973)
[4] Andrianov, A.N.: Modular descent and the Saito-Kurokawa conjecture. Invent. Math.53, 267–280 (1979) · Zbl 0414.10017 · doi:10.1007/BF01389767
[5] Deligne, P.: Theorie de Hodge, I. Actes du Congrès international des Mathématiciens. I, Nice, pp. 425–430 (1970)
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[10] Maass, H.: Über eine Spezialschar von Modulformen zweiten Grades. II. Invent. Math.53, 249–253 (1979) · Zbl 0413.10021 · doi:10.1007/BF01389765
[11] Maass, H.: Über eine Spezialschar von Modulformen zweiten Grades. III. Invent. Math.53, 255–265 (1979) · Zbl 0413.10021 · doi:10.1007/BF01389766
[12] Niwa, S.: Modular forms of half integral weight and the integral of certain theta-functions. Nagoya. Math. J.56, 147–161 (1974) · Zbl 0303.10027
[13] Oda, T.: On modular forms associated with indefinite quadratic forms of signature (2, n). Math. Ann.231, 97–144 (1977) · Zbl 0355.10022 · doi:10.1007/BF01361138
[14] Rallis, S., Schiffman, G.: On a relation between \(\mathop {SL}\limits^ \sim _2 \) cusp forms and cusp forms on the tube domains associated to orthogonal groups. Trans. Am. Math. Soc. (to appear)
[15] Rankin, R.A.: Contributions to the theory of Ramanujan’s function {\(\tau\)}(n) and similar arithmetical functions. I–III. Proc. Cambridge Phil. Soc.35, 351–356, 357–372 (1939), 150–151 (1940) · Zbl 0021.39201 · doi:10.1017/S0305004100021095
[16] Shintani, T.: On construction of holomorphic cusp forms of half integral weight. Nagoya. Math. J.58, 83–126 (1975) · Zbl 0316.10016
[17] Evdokimov, S.A.: A characterization of Maass sapces of paraboloic Siegel modular forms of degree 2. Mat. Sb.112, 133–142 (1980) · Zbl 0433.10014
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