Related papers: Non-commutative Hilbert modular symbols

The goal of this paper is to study the structure of noncommutative weighted shifts, their properties, and to understand their role as models (up to similarity) for $n$-tuples of operators on Hilbert spaces as well as their implications to…

It was shown in previous work that the one-variable $\widehat\mu$-function defined by Zwegers (and Zagier) and his indefinite theta series attached to lattices of signature $(r\!+\!1,1)$ are both Heisenberg harmonic Maa\ss-Jacobi forms. We…

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…

We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the…

Dedekind symbols generalize the classical Dedekind sums (symbols). The symbols are determined uniquely by their reciprocity laws up to an additive constant. There is a natural isomorphism between the space of Dedekind symbols with…

We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times…

Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…

Since their rediscovery in the 1990s, multiple zeta values have become ubiquitous in many areas of mathematics and physics. Their standard integral and sum representations can usually be traced back to a single source, namely the iterated…

The denominator of the Hilbert series of a finitely generated R-module M does not always divide the denominator of the Hilbert series of R. For this reason, we define the universal denominator. The universal denominator of a module M is the…

We generalize the $\mathbb{Z}_2$ invariant of topological insulators using noncommutative differential geometry in two different ways. First, we model Majorana zero modes by KQ-cycles in the framework of analytic K-homology, and we define…

We consider modifications of Manin symbols in first homology groups of modular curves with p-adic integer coefficients for an odd prime p. We show that these symbols generate homology in primitive eigenspaces for the action of diamond…

We study non-holomorphic modular forms built from iterated integrals of holomorphic modular forms for SL$(2,\mathbb Z)$ known as equivariant iterated Eisenstein integrals. A special subclass of them furnishes an equivalent description of…

It is observed that the infinite matrix with entries $(\sqrt{mn}\log (mn))^{-1}$ for $m, n\ge 2$ appears as the matrix of the integral operator $\mathbf{H}f(s):=\int_{1/2}^{+\infty}f(w)(\zeta(w+s)-1)dw$ with respect to the basis…

In this paper we express the multiple Hecke $L$-function in terms of a linear combination of iterated period integrals associated with elliptic cusp forms, which is introduced by Manin around 2004. This expression generalizes the classical…

A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and…

This work gives a version of the Eichler-Shimura isomorphism with a non-abelian $H^1$ in group cohomology. Manin has given a map from vectors of cusp forms to a noncommutative cohomology set by means of iterated integrals. We show Manin's…

This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…

Punctual noncommutative Hilbert schemes are projective varieties parametrizing finite codimensional left ideals in noncommutative formal power series rings. We determine their motives and intersection cohomology, by constructing affine…