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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The Fourier expansion of Eisenstein series for $ {\rm GL}(3,\,{\bf Z})$


Authors: K. Imai and A. Terras
Journal: Trans. Amer. Math. Soc. 273 (1982), 679-694
MSC: Primary 10D20; Secondary 10C15, 22E45
MathSciNet review: 667167
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Abstract: The Fourier expansions of Eisenstein series for $ {\text{GL}}(3,{\mathbf{Z}})$ are obtained by two methods--one analogous to the classical method used by many number theorists, including Weber, in his derivation of the Kronecker limit formula. The other method is analogous to that used by Siegel to obtain Fourier expansions of Eisenstein series for the Siegel modular group. The expansions involve matrix argument $ K$-Bessel functions recently studied by Tom Bengtson. These $ K$-Bessel functions are natural generalizations of the ordinary $ K$-Bessel function which arise when considering harmonic analysis on the symmetric space of the general linear group using a certain system of coordinates.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0667167-5
PII: S 0002-9947(1982)0667167-5
Keywords: Eisenstein series, automorphic forms, general linear group, Fourier expansion, Bruhat decomposition, Bessel functions for the symmetric space of the general linear group
Article copyright: © Copyright 1982 American Mathematical Society