共查询到20条相似文献,搜索用时 546 毫秒
1.
Zhu Fuzu 《数学年刊B辑(英文版)》1994,15(3):349-360
CONSTRUCTIONOFINDECOMPOSABLEDEFINITEHERMITIANFORMS¥ZHUFUZU(DepartmelltofMathematics,EastChinaNormalUniversitytShanghai200062,... 相似文献
2.
V. A. Gritsenko 《Journal of Mathematical Sciences》1987,38(4):2065-2078
One constructs an integral operator, mapping the cusp modular forms of one variable into modular forms relative to Hermitian groups of genus 2 over an imaginary quadratic field. One computes explicitly the Fourier coefficients of the obtained forms.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 51–67, 1985. 相似文献
3.
H. Kim 《Archiv der Mathematik》2002,79(3):208-215
We study multilinear differential operators on a space of Hermitian Jacobi forms as well as on a space of Hermitian modular forms of degree 2. First we define a heat operator and construct multilinear differential operators on a space of Hermitian Jacobi forms of degree 2. As a special case of these operators, we also study Rankin-Cohen type differential operators on a space of Hermitian Jacobi forms. And we construct multilinear differential operators on a space of Hermitian modular forms of degree 2 as an application of multilinear differential operators on Hermitian Jacobi forms. 相似文献
4.
Soumya Das 《Archiv der Mathematik》2010,95(5):423-437
We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show its commutation
with certain Hecke operators and use it to construct a map from elliptic cusp forms to Hermitian Jacobi cusp forms. We construct
Hermitian Jacobi forms as the image of the tensor product of two copies of Jacobi forms and also from the differentiation
of the variables. We determine the number of Fourier coefficients that determine a Hermitian Jacobi form and use the differential
operator to embed a certain subspace of Hermitian Jacobi forms into a direct sum of modular forms for the full modular group. 相似文献
5.
《Journal de Mathématiques Pures et Appliquées》2006,85(5):687-697
We define the Hermitian tangent valued forms of a complex 1-dimensional line bundle equipped with a Hermitian metric. We provide a local characterization of these forms in terms of a local basis and of a local fibred chart. We show that these forms constitute a graded Lie algebra through the Frölicher–Nijenhuis bracket.Moreover, we provide a global characterization of this graded Lie algebra, via a given Hermitian connection, in terms of the tangent valued forms and forms of the base space. The bracket involves the curvature of the given Hermitian connection. 相似文献
6.
Kim (Arch Math (Basel) 79(3):208–215, 2002) constructs multilinear differential operators for Hermitian Jacobi forms and Hermitian modular forms. However, her work relies on incorrect actions of differential operators on spaces of Hermitian Jacobi forms and Hermitian modular forms. In particular, her results are incorrect if the underlying field is the Gaussian number field. We consider more general spaces of Hermitian Jacobi forms and Hermitian modular forms over \(\mathbb {Q}(i)\), which allow us to correct the corresponding results in Kim (2002). 相似文献
7.
Properties of Hermitian forms are used to investigate several natural questions from CR geometry. To each Hermitian symmetric
polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial
product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite
forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including
a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature
pair. 相似文献
8.
We will complete the list of universal binary Hermitian forms over imaginary quadratic fields by investigating three Hermitian forms missed by previous researchers.
9.
Colin TAN 《数学年刊B辑(英文版)》2016,37(1):83-94
Quillen proved that if a Hermitian bihomogeneous polynomial is
strictly positive on the unit sphere,
then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares.
Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from
the eventual positive-definiteness of an associated integral operator. Their
arguments involve asymptotic expansions of the Bergman kernel. The
goal of this article is to give an elementary proof of the
positive-definiteness of this integral operator. 相似文献
10.
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called Dirac operator, which factorizes the Laplacian; monogenic functions may thus also be seen as a generalization of holomorphic functions in the complex plane. Hermitian Clifford analysis offers yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitian (or h-) monogenic functions, of two Hermitian Dirac operators which are invariant under the action of the unitary group. In Brackx et al. (2009) [8] a Clifford-Cauchy integral representation formula for h-monogenic functions has been established in the case of domains with smooth boundary, however the approach followed cannot be extended to the case where the boundary of the considered domain is fractal. At present, we investigate an alternative approach which will enable us to define in this case a Hermitian Cauchy integral over a fractal closed surface, leading to several types of integral representation formulae, including the Cauchy and Borel-Pompeiu representations. 相似文献
11.
J.-F Renard 《Indagationes Mathematicae》2007,18(1):97-134
An analogue of Springer's theorem on the Witt group of quadratic forms over a complete discretely valued field is proved for Hermitian forms over division algebras over a Henselian field, including some cases where the residue characteristic is 2. Residue forms are defined by means of vector space valuations as Hermitian forms on the graded modules associated with the induced filtrations. 相似文献
12.
朱福祖 《中国科学A辑(英文版)》2001,44(1):7-14
Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of
integers Rm of an imaginary quadratic field ℚ(√−m). Using our methods, one can construct explicitly an n-ary nondecomposable positive
definite Hermitian Rm-lattice ( L, h) with given discriminant 2 for every n⩾2 (resp. n⩾13 or odd n⩾3) and square-free m = 12 k + t with k⩾1 and
t∈ (1,7) (resp. k⩾1 and t = 2 or k⩾0 and t∈ 5,10,11). We study also the case for discriminant different from 2. 相似文献
13.
Let E be an imaginary quadratic extension of of class number one. We examine certain representation numbers associated to Hermitian forms over E , which involve counting integral points on flag varieties.
G. Chinta is partially supported by the NSF and by a Humboldt Research Fellowship. 相似文献
14.
Guoping Tang 《K-Theory》1998,13(3):209-267
This article provides the fundamental constructions and results for Hermitian groups which are necessary for an algebraic understanding of the functors K1 and K2 of Hermitian forms. These include a definition of the elementary subgroup EH of a general Hermitian group GH, the Hermitian Whitehead lemma for stabilized GH, a definition of the Hermitian Steinberg group, and the theorem that a stabilized Steinberg group is the universal central extension of its associated stabilized elementary group. 相似文献
15.
《Mathematische Nachrichten》2017,290(2-3):201-217
Hermitian monogenic functions are the null solutions of two complex Dirac type operators. The system of these complex Dirac operators is overdetermined and may be reduced to constraints for the Cauchy datum together with what we called the Hermitian submonogenic system (see [8], [9]). This last system is no longer overdetermined and it has properties that are similar to those of the standard Dirac operator in Euclidean space, such as a Cauchy–Kowalevski extension theorem and Vekua type solutions. In this paper, we investigate plane wave solutions of the Hermitian submonogenic system, leading to the construction of a Cauchy kernel. We also establish a Stokes type formula that, when applied to the Cauchy kernel provides an integral representation formula for Hermitian submonogenic functions. 相似文献
16.
We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence of a prime dividing the (k?1)th generalized Bernoulli number and the existence of non-trivial Hermitian cusp forms of weight k. We will conclude by giving numerical examples for each case. 相似文献
17.
Izu Vaisman 《Annali di Matematica Pura ed Applicata》1982,132(1):1-18
Summary In this paper, we are investigating curvature properties of complex two-dimensional Hermitian manifolds, particularly in the compact case. To do this, we start with the remark that the fundamental form of such a manifold is integrable, and we use the analogy with the locally conformal KÄhler manifolds, which follows from this remark. Among the obtained results, we have the following: a compact Hermitian surface for which either the Riemannian curvature tensor satisfies the KÄhler symmetries or the Hermitian curvature tensor satisfies the Riemannian Bianchi identity is KÄhler; a compact Hermitian surface of constant sectional curvature is a flat KÄhler surface; a compact Hermitian surface M with nonnegative nonidentical zero holomorphie Hermitian bisectional curvature has vanishing plurigenera, c1(M) 0, and no exceptional curves; a compact Hermitian surface with distinguished metric, and positive integral Riemannian scalar curvature has vanishing plurigenera, etc. 相似文献
18.
We construct integral bases for the $SO(3)$-TQFT-modules
of surfaces in genus one and two at roots of unity of
prime order and show that the corresponding mapping class group
representations preserve a unimodular Hermitian form over a ring
of algebraic integers. For higher genus surfaces the Hermitian form
sometimes must be non-unimodular. In one such case,
genus three at a fifth root of unity,
we still give an explicit basis. 相似文献
19.
Yunhee Euh JeongHyeong Park Kouei Sekigawa 《Differential Geometry and its Applications》2013,31(4):463-471
We give an integral formula for the first Pontrjagin number of a compact almost Hermitian surface and derive curvature identities from the integral formula based on the fundamental fact that the first Pontrjagin number in the deRham cohomology group is a topological invariant. Further, we provide some applications of the identities. 相似文献
20.
We will determine (up to equivalence) all of the integral positive definite Hermitian lattices in imaginary quadratic fields of class number 1 that represent all positive integers.