相关论文: An index theorem for gerbes

We introduce an elementary argument to the theory of distribution of sequences modulo one.

The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result by Gromov-Lawson for generalised Dirac operators as well as…

We give a sheaf-theoretic version of the universal coefficient theorem.

The purpose of this article is to provide a version of Bloch-Wigner theorem over the class of rings with many units.

In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.

We give a simple way to extend index-theoretical statements from partial differential operators with smooth coefficients to operators with coefficients of finite Sobolev order.

We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.

We prove several extensions of the Erdos-Fuchs theorem.

I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

In this paper we present theorems and applications of Wallis theorem related to trigonometric integrals.

In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level.

We prove a combination theorem for PD(n)-pairs.

We prove a uniformization theorem in complex algebraic geometry.

We survey the classical results on the prime number theorem

The basic mechanism how gerbes arise in quantum field theory is explained; in particular the case of chiral fermions in background fields is treated. The role of of various gauge group extensions (central extensions of loop groups and their…

New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…

In this paper we prove some interpolation theorems for the multipliers of the Cauchy- Stiltjes type integrals

We give the generating function for the index of integer lattice points, relative to a finite order ideal. The index is an important concept in the theory of border bases, an alternative to Gr\"obner bases. Equivalently, we explicitly solve…

We present a new, elementary, dynamical proof of the prime number theorem.