相关论文: Witt vectors. Part 1

We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology $THH_{C_n}(-)$, and it describes the $E_2$ term of the K\"unneth spectral sequence for…

We describe an algorithm which computes the ring laws for Witt vectors of finite length over a polynomial ring with coefficients in a finite field. This algorithm uses an isomorphism of Illusie in order to compute in an adequate polynomial…

A comparison of results from principal component analysis and support vector machine calculations is made for a variety of phase transitions in two-dimensional classical spin models.

Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities.

We state and prove an identity which represents the most general eta-products of weight 1 by binary quadratic forms. We discuss the utility of binary quadratic forms in finding a multiplicative completion for certain eta-quotients. We then…

In this paper we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of (p,q)th relative Ritt order, (p,q)th relative Ritt type and (p,q)th relative Ritt weak type.

All known elementary vector particles, the photon, Z, W and the gluons, are described by the gauge theory. They belong to the real representation (1/2,1/2) of the Lorentz group. On the other hand inequivalent representations (1,0) and (0,1)…

We give a universal property of the construction of the ring of $p$-typical Witt vectors of a commutative ring, endowed with Witt vectors Frobenius and Verschiebung, and generalize this construction to the derived setting. We define an…

We study the phase diagram of one dimensional spin one-half fermionic cold atoms. The two ``spin'' species can have different hopping or mass. The phase diagram at equal densities of the species is found to be very rich, Mott insulators as…

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…

In part I we introduced the class ${\mathcal E}_2$ of Lie subgroups of $Sp(2,\R)$ and obtained a classification up to conjugation (Theorem 1.1). Here, we determine for which of these groups the restriction of the metaplectic representation…

In arxiv:1602.04254, we have defined polynomial Witt vectors functor from vector spaces over a perfect field $k$ of positive characteristic $p$ to abelian groups. In this paper, we use polynomial Witt vectors to construct a functorial…

The first half of this dissertation reviews the basic notion of vector-valued modular forms and its connection to differential equations. The main purpose of the dissertation is to classify spaces of vector-valued modular forms associated…

The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the values of their first Witt indices is obtained. A number of corollaries of this result are outlined. An investigation of generic Pfister…

In the framework of higher transcendental functions the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here,…

We introduce the good Hilbert functor and prove that it is algebraic. This functor generalizes various versions of the Hilbert moduli problem, such as the multigraded Hilbert scheme and the invariant Hilbert scheme. Moreover, we generalize…

The objective of this article is to give an introduction to p-adic analysis along the lines of Tate's thesis, as well as incorporating material of a more recent vintage, for example Weil groups.

The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the value of their first Witt index is obtained. This result and certain of its corollaries are applied to the study of the weak isotropy index…

This paper presents fundamental algorithms for the computational theory of quadratic forms over number fields. In the first part of the paper, we present algorithms for checking if a given non-degenerate quadratic form over a fixed number…

This is the first one of a series of articles in which we develop the theory of Jacobi forms of lattice index, their close interplay with the arithmetic theory of lattices and the theory of Weil representations. We hope to publish this…