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The Gieseker-Petri divisor in M_g for genus g<=13
Gieseker-Petri divisor M_g for genus g<=13
2011/1/21
The Gieseker-Petri locus GPg is defined as the locus insideMg consisting of curves which violate the Gieseker-Petri Theorem. It is known that GPg has always some divisorial components and it has been ...
Weyl asymptotics of Bisingular Operators and Dirichlet Divisor Problem
Weyl asymptotics of Bisingular Operators Dirichlet Divisor Problem
2011/1/19
We consider a class of pseudodifferential operators defined on the product of two closed manifolds, with crossed vector valued symbols. We study the asymptotic expansion of Weyl counting function of p...
Synchronization of unidirectional time delay chaotic networks and the greatest common divisor
Synchronization unidirectional time delay chaotic networks greatest common divisor
2010/12/28
We present the interplay between synchronization of unidirectional coupled chaotic nodes with
heterogeneous delays and the greatest common divisor (GCD) of loops composing the oriented
graph.
In this paper we study zero-divisor graphs of semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We charact...
On Karatsuba's Problem Concerning the Divisor Function $\tau(n)$
On Karatsuba's Problem the Divisor Function $\tau(n)$
2010/11/11
We study an asymptotic behavior of the sum $\sum\limits_{n\le x}\frac{\D \tau(n)}{\D \tau(n+a)}$. Here $\tau(n)$ denotes the number of divisors of $n$ and $a\ge 1$ is a fixed integer.
In this paper we study linear correlations of the divisor function tau(n) = sum_{d|n} 1 using methods developed by Green and Tao. For example, we obtain an asymptotic for sum_{n,d} tau(n) tau(n+d) ......
For a smooth projective variety P, we construct a Cartier divisor supported on the incidence locus in Ca(P) × Cdim(P)−a−1(P). There is a natural definition of the corresponding line bundle...
The universal theta divisor over the moduli space of curves
universal theta divisor moduli space of curves
2010/11/26
The universal theta divisor over the moduli space Ag of principally polarized abelian varieties of dimension g, is the divisor g inside the universal abelian variety Xg over Ag.