Related papers: Modular properties of Eisenstein series and statis…
We consider the moduli space of holomorphic principal bundles for reductive Lie groups over Riemann surfaces (possibly with boundaries) and equipped with meromorphic connections. We associate to this space a point-wise notion of quantum…
We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain weights.From these, we obtain some…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
The main new result is the computation of the degeneration of l-adic Eisenstein classes at the cusps. This is done by relating it to the degeneration of the elliptic polylog. These classes come from K-theory and their Hodge regulator can…
We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of our efforts to extend in the noncompact…
Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields (see Commun. Math. Phys. 218 (2001)…
We define a theta lift between the homology in degree $N-1$ of a locally symmetric space associated to $\mathrm{SL}_N(\mathbb{R})$ and the space of modular forms of weight $N$, similar to the Kudla-Millson lift in the orthogonal setting. We…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
The contribution, E, of hyperbolic elements to the scalar Casimir energy on a compact quotient of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. Due to the proliferation of prime closed…
We show that for Siegel modular varieties of arbitrary genus, the natural distribution relations satisfied by certain integral Eisenstein cohomology classes defined by Kings admit an adelic refinement. This generalizes the classical…
This paper studies the non-holomorphic Eisenstein series E(z,s) for the modular surface, and shows that integration with respect to certain non-negative measures gives meromorphic functions of s that have all their zeros on the critical…
In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one…
In this article, we show that Fourier eigenmeasures supported on spheres with radii given by a locally finite sequence, which we call $k$-spherical measures, correspond to Fourier series exhibiting a modular-type transformation behaviour…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
Let L >= 3. Using the moduli interpretation, we define certain elliptic modular forms of level Gamma(L) over any field k where 6L is invertible and k contains the Lth roots of unity. These forms generate a graded algebra R_L, which, over C,…
Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and functional equations. Coefficients of these zeta functions are called measures of…
The Euler-Kronecker constants related to congruences of Fourier coefficients of modular forms that have been computed so far, involve logarithmic derivatives of Dirichlet $L$-series as most complicated functions (to the best of our…
Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…