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For a smooth projective variety over a number field, the Beilinson—Bloch conjecture predicts that Chow groups of algebraic cycles modulo rational equivalence can be determined using cohomological data...
Convolution powers of complex functions on Z。
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 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...
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.
Edge growth in graph powers     Edge growth  graph powers       2012/2/29
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...
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...
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...
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...
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...
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...
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...
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.
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 ...

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