共查询到20条相似文献,搜索用时 15 毫秒
1.
《Indagationes Mathematicae》2019,30(6):965-987
We define a generalized hyperbolic Eisenstein series for a pair of a hyperbolic manifold of finite volume and its submanifold. We prove the convergence, the differential equation and the precise spectral expansion associated to the Laplace–Beltrami operator. We also derive the analytic continuation with the location of the possible poles and their residues from the spectral expansion. 相似文献
2.
We give a meromorphic continuation and a functional equationfor the Rankin–Selberg convolution of certain real analyticEisenstein series of half-integral weight. Our result and methodhave several applications to the Koecher–Maass seriesassociated with the real analytic Siegel–Eisenstein series. 相似文献
3.
4.
The family hyperbolic metric for the plumbing variety {zw = t} and the non holomorphic Eisenstein series are combined to provide an explicit expansion for the hyperbolic metrics for degenerating families of Riemann surfaces. Applications
include an asymptotic expansion for the Weil–Petersson metric and a local form of symplectic reduction. 相似文献
5.
Ulrich Terstiege 《manuscripta mathematica》2008,125(2):191-223
We define the notion of antispecial cycles on the Drinfeld upper half plane in analogy to the notion of special cycles in
Kudla and Rapoport (Invent Math 142:153–223, 2000). We determine equations for antispecial cycles and calculate the intersection
multiplicity of two antispecial cycles. The result is applied to calculate the intersection multiplicity of certain degenerate
Hirzebruch–Zagier cycles. Finally we compare this intersection multiplicity to certain representation densities. 相似文献
6.
Bernhard E. Heim 《manuscripta mathematica》2001,106(4):489-503
This paper deals with Jacobi forms Φ on ?×ℂ. The Rankin–Selberg doubling method is employed to study properties of the standard
L-function of Hecke–Jacobi eigenforms. It is shown that every analytic Klingen–Jacobi Eisenstein series attached to Φ has
a meromorphic continuation on the whole complex plane. Hecke–Jacobi cusp eigenforms of weight k > 4 and k≡ 0 mod 4 can written explicitly as a linear combination of theta series. Finally the basis problem of Jacobi forms of square-free
index is solved.
Received: 12 March 2000 / Revised version: 17 September 2001 相似文献
7.
Ulrich Terstiege 《Mathematische Annalen》2011,349(1):161-213
We establish a close connection between the intersection multiplicities of three arithmetic Hirzebruch–Zagier cycles and the
Fourier coefficients of the derivative of a certain Siegel–Eisenstein series at its center of symmetry. Our main result proves
a conjecture of Kudla and Rapoport. 相似文献
8.
Sung-Geun Lim 《The Ramanujan Journal》2009,19(2):121-136
B.C. Berndt (J. Reine Angew. Math. 272:182–193, 1975; 304:332–365, 1978) has derived a number of new transformation formulas, in particular, the transformation formulae of the logarithms of the
classical theta functions, by using a transformation formula for a more general class of Eisenstein series. In this paper,
we continue his study. By using a transformation formula for a class of twisted generalized Eisenstein series, we generalize
a transformation formula given by J. Lehner (Duke Math. J. 8:631–655, 1941) and give a new proof for transformation formulas proved by Y. Yang (Bull. Lond. Math. Soc. 36:671–682, 2004).
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-214-C00003).
This work also partially supported by BK21-Postech CoDiMaRo. 相似文献
9.
Atsushi Ichino 《Mathematische Zeitschrift》2007,255(4):721-729
Following S. S. Kudla and S. Rallis, we extend the Siegel–Weil formula for unitary groups, which relates a value of a Siegel
Eisenstein series to the convergent integral of a theta function. 相似文献
10.
Anders Skovsted Buch Andrew Kresch Mark Shimozono Harry Tamvakis Alexander Yong 《Mathematische Annalen》2008,340(2):359-382
We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of Fomin and Kirillov
(Proc Formal Power Series Alg Comb, 1994) in the basis of stable Grothendieck polynomials for partitions. This gives a common
generalization, as well as new proofs of the rule of Fomin and Greene (Discret Math 193:565–596, 1998) for the expansion of
the stable Schubert polynomials into Schur polynomials, and the K-theoretic Grassmannian Littlewood–Richardson rule of Buch (Acta Math 189(1):37–78, 2002). The proof is based on a generalization
of the Robinson–Schensted and Edelman–Greene insertion algorithms. Our results are applied to prove a number of new formulas
and properties for K-theoretic quiver polynomials, and the Grothendieck polynomials of Lascoux and Schützenberger (C R Acad Sci Paris Ser I Math
294(13):447–450, 1982). In particular, we provide the first K-theoretic analogue of the factor sequence formula of Buch and Fulton (Invent Math 135(3):665–687, 1999) for the cohomological
quiver polynomials. 相似文献
11.
David Burguet 《Inventiones Mathematicae》2011,186(1):191-236
We prove that C2\mathcal{C}^{2} surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet.
Following the strategy of Downarowicz and Maass (Invent. Math. 176:617–636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls
by contracting maps in a approach combining hyperbolic theory and Yomdin’s theory. 相似文献
12.
Pascual Cutillas Ripoll 《Israel Journal of Mathematics》2006,152(1):349-370
Letν′ be the complementary of a point ∞ in a compact Riemann surfaceν. The normal convergence in compact subsets ofν′ of an infinite product of meromorphic functions (with polynomic exponential singularities at ∞ of bounded degree) is shown
in this paper to be equivalent to a certain type of convergence of the double series of Newton sums of the divisors of its
factors. This applies, for instance, to products of Baker functions inν′ and to products of meromorphic functions inν. The result for this last case is also generalized to complementaries of arbitrary nonvoid finite subsets ofν.
Research supported by SA30/00B. 相似文献
13.
Mathias Schulze 《manuscripta mathematica》2007,123(4):373-379
From the degree zero part of the logarithmic vector fields along analgebraic hypersurface singularity we identify the maximal
multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that
all such maximal tori are conjugate and in one–to–one correspondence to maximal tori in the linear jet of the embedded automorphism
group. These results are motivated by Kyoji Saito’s characterization of quasihomogeneity for isolated hypersurface singularities
[Saito in Invent. Math. 14, 123–142 (1971)] and extend previous work with Granger and Schulze [Compos. Math. 142(3), 765–778 (2006), Theorem 5.4] and of Hauser and Müller [Nagoya Math. J. 113, 181–186 (1989), Theorem 4]. 相似文献
14.
Lei Yang 《数学学报(英文版)》2011,27(11):2285-2300
We study the Eisenstein series for a convex cocompact discrete subgroup on a two-dimensional complex hyperbolic space ℍℂ2. We find an inner product formula which gives the connection between Eisenstein series and automorphic Green functions on
a two-dimensional complex hyperbolic space ℍℂ2. As an application of our inner product formula, we obtain the functional equations of Eisenstein series. 相似文献
15.
We prove a limit theorem in the space of meromorphic functions for a new class of general Dirichlet series.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 193–202, April–June, 2006. 相似文献
16.
Axel Ferrari 《manuscripta mathematica》2007,124(3):363-390
Our purpose is to obtain a geometric formula as explicit as possible for the L
2 index of a Dirac operator over a locally symmetric space of finite volume, generalizing Arthur’s formula for the Euler–Poincaré
caracteristic (Arthur in Invent Math 97:257–290, 1989). 相似文献
17.
Takumi Noda 《The Ramanujan Journal》2007,14(3):405-410
We give a sufficient condition of bounded growth for the non-holomorphic Eisenstein series on SL
2(ℤ). The C
∞-automorphic forms of bounded growth are introduced by Sturm (Duke Math. J. 48(2), 327–350, 1981) in the study of automorphic L-functions. We also give a Laplace-Mellin transform of the Fourier coefficients of the Eisenstein series. The transformation
constructs a projection of the Eisenstein series to the space of holomorphic cusp forms.
相似文献
18.
Christopher Svedberg 《Annales Henri Poincare》2011,12(5):849-917
Ringstr?m managed (in Invent Math 173(1):123–208, 2008) to prove future stability of solutions to Einstein’s field equations when matter consists of a scalar field with a potential
creating an accelerated expansion. This was done for a quite wide class of spatially homogeneous space–times. The methods
he used should be applicable also when other kinds of matter fields are added to the stress-energy tensor. This article addresses
the question whether we can obtain stability results similar to those Ringstr?m obtained if we add an electromagnetic field
to the matter content. Before this question can be addressed, more general properties concerning Einstein’s field equation
coupled to a scalar field and an electromagnetic field have to be settled. The most important of these questions are the existence
of a maximal globally hyperbolic development and the Cauchy stability of solutions to the initial value problem. 相似文献
19.
20.
Taejung Kim 《Geometriae Dedicata》2009,140(1):81-93
Krichever (Commun Math Phys 229(2):229–269, 2002) invented the space of matrices parametrizing the cotangent bundle of moduli
space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation
(Hitchin, Duke Math J 54(1):91–114, 1987). We study a necessary and sufficient condition for the linearity of flows on the
space of Krichever–Lax matrices in a Lax representation in terms of cohomological classes using the similar technique and
analysis from the work by Griffiths (Am J Math 107(6):1445–1484, 1985).
相似文献