Related papers: On equivariant class formulas for t-modules
We give a new and very concise proof of the existence of a holomorphic continuation for a large class of twisted multivariable zeta functions. To do this, we use a simple method of "decalage" that avoids using an integral representation of…
We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…
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,…
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…
We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…
Modular invariants satisfy remarkable fusion rules. Let $Z$ be a modular invariant associated to a braided subfactor $N\subset M$. The decomposition of the non-normalized modular invariants $Z Z^{*}$ and $Z^{*}Z$ into sums of normalized…
Twisted current algebras are fixed point subalgebras of current algebras under a finite group action. Special cases include equivariant map algebras and twisted forms of current algebras. Their finite-dimensional simple modules fall into…
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.
This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…
In this paper, we provide a number of subdifferential formulas for a class of nonconvex infimal convolutions in normed spaces. The formulas obtained unify several results on subdifferentials of the distance function and the minimal time…
We extend a classical fact about deformations of groups of units of commutative rings to $\mathbb{E}_{\infty}$-ring spectra, and we use this result to provide a map of spectra generalizing the ordinary logarithmic derivative induced by an…
We compute the equivariant zeta function for bundles over infinite graphs and for infinite covers. In particular, we give a ``transfer formula'' for the zeta function of infinite graph covers. Also, when the infinite cover is given as a…
We prove thin-thick decompositions, for the class of Hardy martingales and thereby strengthen its square function characterization. We apply the underlying method to several classical martingale inequalities, for which we give new proofs .
This work is an example driven overview article of recent works on the connection of multiple zeta values, modular forms and q-analogues of multiple zeta values given by multiple Eisenstein series.
The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to define the valued analogue of natural quiver, called {\em natural…
In this paper, we obtain Atkin--Lehner decompositions for spaces of modular forms on definite quaternion algebras. Similar to Casselman's approach our methods are representation theoretic. Using Jacquet--Langlands correspondence we also…
We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.
We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.
We propose a formulation of the Equivariant Tamagawa Number Conjecture for modular motives with coefficients in universal deformation rings and Hecke algebras; something which seems to have been heretofore missing because the complexes of…