Related papers: Higher-Weight Limiting Modular Symbols

We define and study the space of mixed modular symbols for a given finite index subgroup $\Gamma$ of $SL_2(\mathbf{Z})$. This is an extension of the usual space of modular symbols, which in some cases carries more information about…

We develop a theory of pseudo-differential operators associated with the gyrator transform on modulation spaces. The gyrator transform is a two-dimensional linear canonical transform which can be viewed as a rotation in the time-frequency…

This work provides the first step toward the classification of irreducible finite weight modules over twisted affine Lie superalgebras. We study all such modules whether the canonical central element acts as a nonzero multiple of the…

We give a new interpretation of Stark units associated to real quadratic fields as real multiplication values of a modular cocycle. The cocycle of interest is a meromorphic factor describing the modular transformations of the $q$-Pochhammer…

For proper stacks, unlike schemes, there is a distinction between rational and integral points. Moreover, rational points have extra automorphism groups. We show that these distinctions exactly account for the lower order main terms…

This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the…

We consider a geometric theta correspondence from the first homology of a modular curve, to modular forms of weight $2$. Using Stevens' description of the homology, we find that this map sends modular symbols to product of weight one…

We consider Marcinkiewicz multipliers of any lacunary order defined by means of uniformly bounded variation on each lacunary Littlewood--Paley interval of some fixed order $\tau\geq 1$. We prove the optimal endpoint bounds for such…

The paper deals with unbounded composition operators with infinite matrix symbols acting in $L^2$-spaces with respect to the gaussian measure on $\mathbb{R}^\infty$. We introduce weak cohyponormality classes $\EuScript{S}_{n,r}^*$ of…

We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…

In this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras $A(\infty)$, $B(\infty)$, $C(\infty)$ and $D(\infty)$. Our main tool…

The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To…

The main aim of this paper is to provide a method which allows finding limiting shapes of symbolic generic initial systems of higher-dimensional subvarieties of P^n. M. Mustata and S. Mayes established a connection between volumes of…

Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present…

In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…

We generalize the results of [KMST] concerning equivariant quantization by means of Verma modules $M(\lambda)$ for generic weight $\lambda$ to the case of general $\lambda$. We consider the relationship between the Shapovalov form on an…

We prove, by use of inductive techniques, that assorted unbounded composition operators in $L^2$-spaces with matrical symbols are cosubnormal.

We study relations between the classical modular symbols associated with congruence subgroups and Kontsevich-Pestun-Tschinkel groups $\mathcal{M}_n(G)$ associated with finite abelian groups $G$.

We show that the support of an irreducible weight module over the $W$-algebra $W(2, 2)$, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite…

In this paper, we study irreducible weight modules with infinite dimensional weight spaces over the mirror-twisted Heisenberg-Virasoro algebra $\mathcal{D}$. More precisely, the necessary and sufficient conditions for the tensor products of…