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Symbolic powers versus regular powers of ideals of general points in P^1 x P^1
symbolic powers multigraded points
2011/9/20
Abstract: Let I be a homogeneous ideal of R = k[x_0,...,x_n]. A current research theme is to compare the symbolic powers of I with the regular powers of I. In this paper, we investigate which ordinary...
Sieve methods in group theory I: Powers in Linear groups
Sieve Property-T Powers Linear groups Finite groups of Lie type
2011/9/14
Abstract: A general sieve method for groups is formulated. It enables one to "measure" subsets of a finitely generated group. As an application we show that if $\Gamma$ is a finitely generated non vir...
Stein's method and the multivariate CLT for traces of powers on the classical compact groups
random matrices compact Lie groups Haar measure traces of powers Stein’s method
2011/2/22
Let Mn be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix ...
Powers of lexsegment ideals with linear resolution
Powers of lexsegment ideals linear resolution
2010/11/15
All powers of lexsegment ideals with linear resolution (equivalently, with linear quotients) have linear quotients with respect to suitable orders of the minimal monomial generators. For a large subc...
Some new super-congruences modulo prime powers
super-congruences modulo prime powers math
2010/11/22
Let $p>3$ be a prime. We show that $$\sum_{k=0}^{p-1}\binom(-1/(p+1),k)^{p+1}=0 (mod p^5).$$ For any positive integer m not divisible by p, we prove that $$\sum_{k=0}^{p-1}(-1)^{km}\binom(p/m-1,k)^m=0...
Existence of translating solutions to the flow by powers of mean curvature on unbounded domains
Dirichlet problem mean curvature flow elliptic equation unbounded domain.
2010/12/7
In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain in Rn(n ≥ 2). T...
A Lower Bound for the Differences of Powers of Linear Operators
Esterle--Berkani's conjecture Quasi-nilpotent linear operator Differences of powers Decay
2007/12/11
Let $T$ be a bounded linear operator in a Banach space, with $\sigma(T) = \{1\}$. In 1983, Esterle--Berkani' s conjecture was proposed for the decay of differences $\left ( I - T \right ) T\sp{n}$ as ...
The Waring-goldbach Problem for Unlike Powers
Waring--Goldbach problem Circle method Exceptional set
2007/12/10
In this paper, it is proved that with at most $O(N^{\frac{65}{66}})$ exceptions, all even positive integers up to $N$ are expressible in the form $p_2^2+p_3^3+p_4^4+p_5^5$. This improves a recent resu...