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An elementary approach to Hecke operators. (English) Zbl 0251.10022

MSC:

11F27 Theta series; Weil representation; theta correspondences
32N15 Automorphic functions in symmetric domains
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References:

[1] Hecke, E.: Über Modulfunktionen und die Dirichletschen Reihen mit Eulersche Producktentwicklung, I, II. Math. Ann.114, 1-28, 316-351 (1937) · Zbl 0015.40202 · doi:10.1007/BF01594160
[2] Koecher, M.: Zur Operatorentheorie der Modulformenn-ten Grades. Math. Ann.130, 351-385 (1956) · Zbl 0073.30503 · doi:10.1007/BF01343231
[3] Lippa, E.: Hecke operators for modular forms of genusr. Ph. D. dissertation, University of Michigan, May 1971
[4] Maass, H.: Die Primazahlen in der Theorie der Siegelschen Modulfunktionen. Math. Ann.124, 87-122 (1951) · Zbl 0044.30901 · doi:10.1007/BF01343553
[5] Satake, I.: Theory of spherical functions on reductive algebraic groups over \(\mathfrak{P}\) -adic fields. I.H.E.S. Publications Mathématiques18, 5-70 (1963) · Zbl 0122.28501
[6] Shimura, G.: On modular correspondences for SP (N, ?) and their congruence relations. Proc. N.A.S.49, 824-828 (1963) · Zbl 0122.08803 · doi:10.1073/pnas.49.6.824
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