Voronoi formulas on GL ( n )

Automorphic distributions , L - functions , and Voronoi summation for GL

for the error term in Gauss’ classical circle problem, improving greatly on Gauss’ own bound O(x1/2). Though Voronoi originally deduced his formulas from Poisson summation in R2, applied to appropriately chosen test functions, one nowadays views his formulas as identities involving the Fourier coefficients of modular forms on GL(2), i.e., modular forms on the complex upper half plane. A discuss...

PLANCHEREL MEASURE FOR GL(n): EXPLICIT FORMULAS AND BERNSTEIN DECOMPOSITION

Let F be a nonarchimedean local field, let GL(n) = GL(n, F ) and let ν denote Plancherel measure for GL(n). Let Ω be a component in the Bernstein variety Ω(GL(n)). Then Ω yields its fundamental invariants: the cardinality q of the residue field of F , the sizes m1, . . . ,mt, exponents e1, . . . , et, torsion numbers r1, . . . , rt, formal degrees d1, . . . , dt and the Artin conductors f11, . ...

Hall-littlewood Vertex Operators and Generalized Kostka Polynomials Mark Shimozono and Mike Zabrocki

Kostka-Folkes polynomials may be considered as coefficients of the formal power series representing the character of certain graded GL(n)-modules. These GL(n)-modules are defined by twisting the coordinate ring of the nullcone by a suitable line bundle [1] and the definition may be generalized by twisting the coordinate ring of any nilpotent conjugacy closure in gl(n) by a suitable vector bundl...

Automorphic Distributions, L-functions, and Voronoi Summation for GL(3)

A ug 2 00 4 Automorphic Distributions , L - functions , and Voronoi Summation for GL ( 3 )