p-adic超几何函数与Dwork超曲面上的有理点

p-adic超几何函数是经典的Gauss超几何函数在有限域上的模拟,与许多数论问题都有联系.设Fq是q元有限域,λ∈Fq,n为正整数.本文研究了Dwork超曲面Dλ^n:x1^n+x2^n+…+xn^n=nλx1x2…xn及其推广形式上的Fq-有理点,并在n与q(q-1)互素时给出了由p-adic超几何函数表示的各种Fq-有理点个数的公式,从而修正和改进了Barman与Goodson等人的结论.     

The Laguerre pseudospectral method for the radial Schrödinger equation

By transforming dependent and independent variables, radial Schrödinger equation is converted into a form resembling the Laguerre differential equation. Therefore, energy eigenvalues and wavefunctions of M-dimensional radial Schrödinger equation with a wide range of isotropic potentials are obtained numerically by using Laguerre pseudospectral methods. Comparison with the results from literature shows that the method is highly competitive.     

Asymptotics and weighted estimates of meixner polynomials orthogonal on the gird {0, δ, 2δ, ...}

Suppose that 0<δ≤1,N=1/δ, and α, ga≥0, is an integer. For the classical Meixner polynomials orthonormal on the gird {0, δ, 2δ, ...} with weight ρ(x)=(1-e ^−δ)^αг(Nx+α+ 1)/г(Nx+1), the following asymptotic formula is obtained: . The remainderv _n,N ^α (z) forn≤λN satisfies the estimate

Isometric Deformations of Compact Hypersurfaces

In 1955 N. Kuiper and J. Nash proved that given a C embeddingF of a C Riemannian n -manifold (M,g) in E ⁿ⁺¹ which is short in the sense that the metric induced by F is less thang, there is a C ¹ isometric embedding which is arbitrarily C ⁰-close to F. We extend the Nash--Kuiper result for compact M to the case of deformations. In other words, we prove that given a continuous family of short C embeddings ( ) of a compact Riemannian n-manifold M , there is an isometric deformation through C ¹ embeddings which is C ⁰ -close to F. With more assumptions which are typically met in practice, this result is shown to hold in the more difficult case where F(s) is short for s>0 andF(0) is isometric. We use this to prove that if a C convex hypersurface is sufficiently close to being planar in an average sense (e.g. an oblate spheroid in E ³ with axis ratio more than , then it admits an isometric deformation which increases the enclosed volume.     

Complexity of tensor products of modules and a theorem of Huneke-Wiegand

This paper concerns the notion of complexity, a measure of the growth of the Betti numbers of a module. We show that over a complete intersection the complexity of the tensor product of two finitely generated modules is the sum of the complexities of each if for . One of the applications is simplification of the proofs of central results in a paper of C. Huneke and R. Wiegand on the tensor product of modules and the rigidity of Tor.