Weyl group multiple Dirichlet series III:: Eisenstein series and twisted unstable Ar

被引:27
作者
Brubaker, B. [1 ]
Bump, D. [2 ]
Friedberg, S. [3 ]
Hoffstein, J. [4 ]
机构
[1] MIT, Cambridge, MA 02139 USA
[2] Stanford Univ, Stanford, CA 94305 USA
[3] Boston Coll, Chestnut Hill, MA 02167 USA
[4] Brown Univ, Providence, RI 02912 USA
关键词
D O I
10.4007/annals.2007.166.293
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Weyl group multiple Dirichlet series were associated with a root system Phi and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] and Brubaker, Bump and Friedberg [4] provided n is sufficiently large; their coefficients involve n-th order Gauss sums. The case where n is small is harder, and is addressed in this paper when Phi = A(r). "Twisted" Dirichet series are considered, which contain the series of [4] as a special case. These series are not Euler products, but due to the twisted multiplicativity of their coefficients, they are determined by their p-parts. The p-part is given as a sum,of products of Gauss sums, parametrized by strict Gelfand-Tsetlin patterns. It is conjectured that these multiple Dirichlet series are Whittaker coefficients of Eisenstein series on the n-fold metaplectic cover of GL(r+1), and this is proved if r = 2 or n = 1. The equivalence of our definition with that of Chinta [11] when n = 2 and r <= 5 is also established.
引用
收藏
页码:293 / 316
页数:24
相关论文
共 22 条
[1]  
Bass H., 1967, PUBL MATH-PARIS, V33, P59, DOI DOI 10.1007/BF02684586
[2]  
Borel A., 1979, P S PURE MATH 2, P27
[3]  
BRUBAKER B, IN PRESS PROGR MATH, V258
[4]  
BRUBAKER B, METAPLECTIC EISENSTE
[5]  
BRUBAKER B, GELFAND TSETLIN INTE
[6]   Weyl group multiple Dirichlet series II: The stable case [J].
Brubaker, Ben ;
Bump, Daniel ;
Friedberg, Solomon .
INVENTIONES MATHEMATICAE, 2006, 165 (02) :325-355
[7]  
Brubaker B, 2006, P SYMP PURE MATH, V75, P91
[8]   On some applications of automorphic forms to number theory [J].
Bump, D ;
Friedberg, S ;
Hoffstein, J .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 33 (02) :157-175
[9]  
BUMP D, 1984, LECT NOTES MATH, V1083, pR1
[10]  
CASSELMAN W, 1980, COMPOS MATH, V41, P207