Spherical Functions on a Group of $p\text{-adic}$ Type

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

Last update: 13 February 2014

References

[AMa1969] M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, Massachusetts, 1969.

[Bou1968] N. Bourbaki, Groupes et Algébres de Lie, Chapitres 4, 5 et 6, Eléments de Mathématique, 34, Hermann, Paris, (1968). MR 39:1590

[BTi1966] F. Bruhat and J. Tits, 4 notes in Comptes Rendus vol. 263 (1966), 766-768; 822-825; 867-869.

[BTi1967] F. Bruhat and J. Tits, Groupes algèbriques simples sur un corps local, in Proceedings of a Conference on Local Fields, Springer (1967).

[Die1967] H. Dieudonné, Treatise on Analysis, Vol. II, Academic Press (1967).

[GKa1962] S. G. Gindikin and F. I. Karpelevic, Plancherel measure of Riemannian symmetric spaces of non-positive curvature, Soviet Math. 3 (1962), 962-965.

[God1957] R. Godement, Introduction aux travaux de A. Selberg, Sém. Bourbaki (1957), Exp. 144.

[God1952] R. Godement, A theory of spherical functions I, Trans. A.M.S. vol. 73 (1952), 496-556.

[Har1958] Harish-Chandra, Spherical functions on a semi-simple Lie group I, Amer. J. Math. 80 (1958), 241-310.

[Hel1962] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press (1962).

[HJo1969] S. Helgason and K. Johnson, The bounded spherical functions on symmetric spaces, Advances in Math. 3 (1969), 586-593.

[Mac1968-2] I.G. Macdonald, Spherical functions on a $p\text{-adic}$ Chevalley group, Bull. A.M.S. 74 (1968), 520-525.

[Mat1969] H. Hatsumoto, Functions sphériques sur un groupe semi-simple $p\text{-adique}$, Comptes Rendus 269 (1969), 829-832.

[Sat1963] I. Satake, Theory of spherical functions on reductive algebraic groups over $p\text{-adic}$ fields, Publ. Math. I.H.E.S. no. 18 (1963), 1-69.

[Ste1967] R. Steinberg, Lectures notes on Chevalley groups, Yale University, (1967).

[Tam1960] T. Tamagawa, On Selberg's trace formula, J. Fac. Sci., Univ. of Tokyo 8 (1960), 363-386.

[Tat1967] J.T. Tate, Fourier analysis in number fields and Hecke's zeta-functions, reproduced in Algebraic Number Theory (eds. J.W.S.-Cassels and A. Fröhlich), Academic Press (1967).

Notes and references

This is a typed version of the book Spherical Functions on a Group of $p\text{-adic}$ Type by I. G. Macdonald, Magdalen College, University of Oxford. This book is copyright the University of Madras, Madras 5, India and was first published November 1971.

Published by the Ramanujan Institute, University of Madras, and printed at the Baptist Mission Press, 41A Acharyya Jagadish Bose Road, Calcutta 17, India.

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