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Garland, Howard

Absolute convergence of Eisenstein series on loop groups. (English) Zbl 1160.11025

Duke Math. J. 135, No. 2, 203-260 (2006).
In earlier work [Studies in Mathematics. Tata Inst. Fundam. Res. 17, 275–319 (2004; Zbl 1157.11314)], the author established the a.e. convergence of certain Eisenstein series on arithmetic quotients of loop groups. In this article he proves that these series converge everywhere, and uniformly on certain bounded sets.

Cited in 8 Documents

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E67 Loop groups and related constructions, group-theoretic treatment

Citations:

Zbl 1157.11314
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\textit{H. Garland}, Duke Math. J. 135, No. 2, 203--260 (2006; Zbl 1160.11025)
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References:

[1] H. Garland, The arithmetic theory of loop algebras , J. Algebra 53 (1978), 480–551.; Erratum , J. Algebra 63 (1980), 285. \(\!\); Mathematical Reviews (MathSciNet): · Zbl 0383.17012
[2] -, The arithmetic theory of loop groups , Inst. Hautes Études Sci. Publ. Math. 52 (1980), 5–136. · Zbl 0475.17004
[3] -, The arithmetic theory of loop groups, II: The Hilbert-modular case , J. Algebra 209 (1998), 446–532. · Zbl 0974.22020
[4] -, “Certain Eisenstein series on loop groups: Convergence and the constant term” in Algebraic Groups and Arithmetic (Mumbai, 2001) , Tata Inst. Fund. Res., Mumbai, 2004.
[5] -, “Eisenstein series on loop groups: Maass-Selberg relations 1” to appear in Algebraic Groups and Homogeneous Spaces (Mumbai, 2004) , Tata Inst. Fund. Res., Mumbai.
[6] -, Eisenstein series on loop groups: Maass-Selberg relations 2 , to appear in Amer. J. Math.
[7] -, Eisenstein series on loop groups: Maass-Selberg relations 3 , to appear in Amer. J. Math.
[8] -, Eisenstein series on loop groups: Maass-Selberg relations 4 , in preparation.
[9] N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of \(p\) -adic Chevalley groups , Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5–48. · Zbl 0228.20015
[10] F. Shahidi, Infinite dimensional groups and automorphic \(L\)-functions , Pure Appl. Math. Q. 1 (2005), 683–699. · Zbl 1203.11041
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