相关论文: Round about Kudla's Green function for $\textrm{SO…

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.

We give a thorough analysis of those subgroups of SO(3) generated by rotations about perpendicular axes by 2\pi/p and 2\pi/q. A corollary is that such a group is the free product of the cyclic groups of rotations about the separate axes if…

The article generalizes an observation of Zagier and Gangl to show that the image of the spectral Eisenstein series on a general congruence subgroup of $\text{SL}_2(\mathbb{Z})$, under the Eichler-Shimura isomorphism, is defined over a…

A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo…

In this paper, we consider the set of r-symbols in a full generality. We construct Hall-Littlewood functions and Kostka functions associated to those r-symbols. We also discuss a multi-parameter version of those functions. We show that…

We consider families of special cycles, as introduced by Kudla, on Shimura varieties attached to anisotropic quadratic spaces over totally real fields. By augmenting these cycles with Green currents, we obtain classes in the arithmetic Chow…

Subconvexity bounds are proved for general Epstein zeta functions of k-ary quadratic forms. This is related to sup-norm bounds for Eisenstein series on GL(k), and the exact sup-norm exponent is determined to be (k-2)/8 for k >= 2. In…

Our aim is to clarify the relationship between Kudla's and Bruinier's Green functions attached to special cycles on Shimura varieties of orthogonal and unitary type. These functions play a key role in the arithmetic geometry of the special…

For a chordal SLE$_\kappa$ ($\kappa\in(0,8)$) curve in a domain $D$, the $n$-point Green's function valued at distinct points $z_1,\dots,z_n\in D$ is defined to be $$G(z_1,\dots,z_n)=\lim_{r_1,\dots,r_n\downarrow 0} \prod_{k=1}^n r_k^{d-2}…

We use Green's canonical syzygy conjecture for generic curves to prove that the Green-Lazarsfeld gonality conjecture holds for generic curves of genus g, and gonality d, if $g/3<d<[g/2]+2$.

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

We describe the application of the results of Kudla-Millson on the modularity of generating series for cohomology classes of special cycles to the case of lattice polarized K3 surfaces. In this case, the special cycles can be interpreted as…

In this paper we will study certain models of irreducible admissible representations of the split special orthogonal group $SO(2n+1)$ over a nonarchimedean local field. If $n=1$, these models were considered by Waldspurger. If $n=2$, they…

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of…

An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…

We consider the Kudla-Millson theta series associated to a quadratic space of signature $(N,N)$. By combining a `see-saw' argument with the Siegel-Weil formula, we show that its (regularized) integral along a torus attached to a totally…

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. We generalize the Kudla-Millson relation between intersection numbers of cycles and Fourier coefficients of Siegel…

We study nearly holomorphic Siegel Eisenstein series of general levels and characters on $\mathbb{H}_{2n}$, the Siegel upper half space of degree $2n$. We prove that the Fourier coefficients of these Eisenstein series (once suitably…

We present a new formalism for describing solutions of the one-dimensional stationary Schr\"odinger equation in terms of the Lie group SL(3,C) and its Lie algebra. In this formalism, we obtain a universal expression for the Green function…