We introduce certain special functions ("Shintani functions") on GL(n) over a non-Archimedean local field. We prove the uniqueness, existence and partial explicit formula of Shintani functions. We give several applications of these local results to the theory of automorphic L-functions for GL(n).
We prove that there exist complete minimal surfaces in the Euclidean 3-space with one Enneper-type end and finite total curvature which have two parametersj, k and are of genus jk , where j and k are positive integers. Our main problem is the period problem: each surface has j periods to be killed. We prove that these periods can be killed simultaneously.
We show that a certain Riesz-product type measure is singular. This proves the singularity of the spectral measures of a certain ergodic transformation, known as the staircase.
The aim of this paper is to prove a type of uniqueness for the Dirichlet problem on a cylinder the special case of which is a strip in the plane. By defining generalized Poisson integrals with certain continuous functions on the boundary of a cylinder, we shall investigate the difference between them and harmonic functions having the same boundary value. Given any continuous function on the boundary of a cylinder, we shall also give a harmonic function with that function as the boundary value.
Abstract. We give an upper bound for the infimum of the essential spectrum of the combinatorial Laplacian on an infinite graph in terms of the exponential growth of the graph.
It is well known that the classical skew Schur module is isomorphic to a direct sum of (non-skew) Schur modules, the multiplicities being given by the Littlewood-Richardson rule. We define a multiparameter quantum deformation of the classical skew Schur module, and show that up to a filtration, it still has a Littlewood-Richardson decomposition. The ground ring can be any commutative ring, and q is allowed to be a root of 1.