Related papers: Theta operators on Hodge type Shimura varieties

We describe a computational approach to the verification of Maeda's conjecture for the Hecke operator T2 on the space of cusp forms of level one. We provide experimental evidence for all weights less than 12000, as well as some applications…

We consider the topological sigma-model on Riemann surfaces with genus g and h holes, and target space CP1. We calculate the correlation functions of bulk and boundary operators, and study the symmetries of the model and its most general…

For a prime $p$ and a commutative ring $R$ with unity, let $W(R)$ denote the group of $p$-typical Witt vectors. The group $W(R)$ is endowed with a Verschiebung operator $V: W(R)\to W(R)$ and a Teichm\"{u}ller map $\langle \ \rangle:…

A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a…

Let $p$ be an odd prime and $f$ be a nearly ordinary Hilbert modular Hecke eigenform defined over a totally real field $F$. Let $\mathbb{I}$ be an irreducible component of the universal nearly ordinary or locally cyclotomic deformation of…

In this paper, we first introduce several new classes of weighted amalgam spaces. Then we discuss both strong type and weak type estimates for certain multilinear $\theta$-type Calder\'on--Zygmund operators $T_\theta$ recently introduced in…

We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to the metric. The main result of this paper is a generalized…

Let (S,H) be a rational algebraic surface with an ample divisor. We compute generating functions for the Hodge numbers of the moduli spaces of H-stable rank 2 sheaves on S in terms of certain theta functions for indefinite lattices that…

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…

Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some…

This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…

We present a transplantation theorem for Jacobi coefficients in weighted spaces. In fact, by using a discrete vector-valued local Calder\'{o}n-Zygmund theory, which has recently been furnished, we prove the boundedness of transplantation…

We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…

Norm-compatible families of cohomology classes for Shimura varieties, and other arithmetic symmetric spaces, play an important role in Iwasawa theory of automorphic forms. The aim of this note is to give a systematic approach to proving…

This article surveys some recent work of the author on Hilbert modular fourfolds X. After some preliminaries on the cohomology and special, codimension 2 cycles Z on X of Hirzebruch-Zagier type, a proof of the Tate conjecture for X over…

An RD-space $\mathcal{X}$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\mathcal{X}$. In this setting, the authors establish the boundedness of…

We prove multiplicity one for vector valued holomorphic Siegel modular forms of weights greater or equal to 3 and the full Siegel modular group and give a trace formula for the action of the Hecke operators T(p) in the regular cases.

Every four-dimensional ${\cal N}=2$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected…

In a recent work, the author has constructed two families of algebraic cycles in Bloch cycle algebra over the prjective line minus 3 points that are expected to correspond to multiple polylogarithms in one variable and have a good…

We formulate characteristic $p$ analogues of the Mumford--Tate and the Andr\'e--Oort conjectures for ordinary mod $p$ Shimura varieties of Hodge type, and set up general frameworks for studying them. We prove the two conjectures for…