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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars:Vanishing of some algebraic cycles on powers of Shimura curves
志村曲线 幂 代数 循环消失
2023/4/27
Convolution powers of complex functions on Z。
Congruences of Multipartition Functions Modulo Powers of Primes
modular form partition multipartition Ramanujan-type congruence
2014/6/3
Let pr(n) denote the number of r-component multipartitions of n, and let Sγ λ be the space spanned by η(24z)γφ(24z), where η(z) is the Dedekind’s eta function and η(z) is a holomorphic modular form i...
A Duality Between Non-Archimedean Uniform Spaces and Subdirect Powers of Full Clones
Uniform Space Duality Hyperspace Variety
2012/7/11
A uniform space is said to be non-Archimedean if it is generated by equivalence relations. If $\lambda$ is a cardinal, then a non-Archimedean uniform space $(X,\mathcal{U})$ is $\lambda$-totally bound...
This note deals with the relationship between the total number of $k$-walks in a graph, and the sum of the $k$-th powers of its vertex degrees. In particular, it is shown that the the number of all $k...
L^2-norms of exponential sums over prime powers
Primes in short intervals Diophantine problems with primes Number Theory
2012/6/14
We study a suitable mean-square average of primes in short intervals, generalizing Saffari-Vaughan's result. We then apply it to a ternary Diophantine problem with prime variables.
For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth p...
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...
Simple Spectrum for Tensor Products of Mixing Map Powers
Tensor Products Mixing Map Powers Dynamical Systems
2011/9/20
Abstract: We prove the existence of a mixing rank one map $T$ such that the product $T\otimes T^2\otimes T^3\otimes...$ has simple spectrum. This result is used in S.V. Thikhonov's proof of the existe...
Representation of powers by polynomials over function fields and a problem of Logic
problem of Logic polynomials over function fields Number Theory
2011/9/15
Abstract: We solve a generalization of B\"uchi's problem in any exponent for function fields, and briefly discuss some consequences on undecidability. This provides the first example where this proble...
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...
Convolution powers in the operator-valued framework
Convolution powers the operator-valued framework Operator Algebras
2011/9/9
Abstract: We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers wit...
A note on the minimum skew rank of powers of paths
minimum skew rank path (strict) power of a graph Combinatorics
2011/9/5
Abstract: The real minimum skew rank of a simple graph G is the smallest possible rank among all real skew symmetric matrices, whose (i,j)-entry (for i not equal to j) is nonzero whenever {i, j} is an...
The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring
Almost Complete Intersection Enumeration of Plane Partitions
2011/1/18
Let k be a field. For each pair of positive integers (n,N), we resolve Q = R/(xN, yN, zN) as a module over the ring R = k[x, y, z]/(xn +yn + zn). Write N in the form N = an + r for integers a and r.
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 ...