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References
Atkin, A. O. L., Lehner, J.: Hecke operators on Λ0(m). Math. Ann.185, 134–160 (1970).
Baily, W., Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains. Ann. of Math.84, 442–528 (1966).
Casselman, W.: On abelian varieties with many endomorphisms and a conjecture of Shimura's, Inventiones math.12, 225–236 (1971).
Jacquet, H., Langlands, R. P.: Automorphic forms on GL(2). Berlin-Heidelberg-New York: Springer Lecture Notes, No.114, 1970.
Langlands, R. P.: Problems in the theory of automorphic forms, 18–86. In: Berlin-Heidelberg-New York: Springer Lecture Notes, No.170, 1970.
Miyake, T.: On automorphic forms onGL 2 and Hecke operators. Ann. of Math.94, 174–189 (1971).
Ogg, A.: Functional equations of modular forms. Math. Ann.183, 337–340 (1969).
Ogg, A.: On a convolution ofL-series. Inventiones math.7, 297–312 (1969).
Rankin, R.: Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions. II. Proc. Camb. Phil. Soc.35, 357–372 (1939).
Satake, I.: Theory of spherical functions on reductive algebraic groups overp-adic fields. Publications Mathematiques I.H.E.S. No. 18.
Weil, A.: Dirichlet series and automorphic forms. Berlin-Heidelberg-New York: Springer Lecture Notes. No.189, 1971.
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Since submitting this, I have come across a paper by M. E. Novodvorskii, “On certain invariant vectors of infinite dimensional representations of Chevalley groups”, Functional Analysis and Its Applications, Vol. 5 (1971), pp. 87–88 (in Russian), which contains my Theorem 1 below. The proof he indicates is much simpler than mine, but not exhibiting any relationship to the zeta function.
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Casselman, W. On some results of Atkin and Lehner. Math. Ann. 201, 301–314 (1973). https://doi.org/10.1007/BF01428197
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DOI: https://doi.org/10.1007/BF01428197