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References for Chapter I
The Weil representation is constructed in
Weil, A., Sur certains groupes d'opérateurs unitaires, Acta Math., t. 111, 1964.
One of the first to study representations of groups over non-archimedean local fields was F. Mautner in
Mautner, F., Spherical functions over g — adic fields, I, Amer. Jour. Math., vol LXXX, 1958.
Absolutely cuspidal representations were first constucted by Gelfand and Graev. References to their work and that of Kirillov will be found in
Gelfand, I.M., M.I. Graev, and I.I. Pyatetskii — Shapiro, Representation Theory and Automorphic Functions, W.B. Saunders Co., 1966.
These representations were constructed in terms of the Weil representation by Shalika and by Tanaka.
Shalika, J. Representations of the two-by-two unimodular group over local fields, Notes, Institute for Advanced Study.
Tanaka, S., On irreducible unitary representations of some special linear groups of the second order, Osaka Jour. Math., 1966.
To classify the representations over an archimedean field we have used a theorem of Harish-Chandra which may be found in
Harish-Chandra, Representations of semisimple Lie groups, II, T.A.M.S., vol 76, 1954.
Our discussion of characters owes much to
Sally, P.J. and J.A. Shalika, Characters of the discrete series of representations of SL(2) over a local field, P.N.A.S., 1968.
Three standard references to the theory of L — functions are
Lang, S., Algebraic numbers, Addison-Wesley, 1964.
Tate, J., Fourier analysis in number fields and Hecke's Zeta — functions in Algebraic number theory, Thompson Book Co., 1967.
Weil, A., Basic number theory, Springer Verlag, 1967.
In Paragraph 8 we have used a result from
Harish-Chandra, Automorphic forms on semisimple Lie groups, Springer-Verlag, 1968.
Tamagawa measures are discussed in
Weil, A. Adèles and algebraic groups, Institute for Advanced Study, 1961.
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Jacquet, H., Langlands, R.P. (1970). Local Theory. In: Automorphic Forms on GL (2). Lecture Notes in Mathematics, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058989
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DOI: https://doi.org/10.1007/BFb0058989
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