Let F be a totally real field and p rational prime unramified in F. We prove partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to subset of weights, an form partially classical. use method analytic continuation.

We introduce and study certain hyperbolic versions of automorphic Lie algebras related to the modular group. Let $\Gamma$ be a finite index subgroup $\mathrm{SL}(2,\mathbb{Z})$ with an action on complex simple algebra $\mathfrak g$, which can extended $\mathrm{SL}(2,\mathbb{C})$. show that corresponding $\mathfrak{g}$-valued forms is isomorphic extension $\mathfrak{g}$ over usual forms. This es...

Certain objects of conformal field theory, for example partition functions on the rectangle and torus, one-point are either invariant or transform simply under modular group, properties which should be preserved $T\overline T$ deformation. The formulation proof this statement in fact extents to more general such as deformed Jacobi forms. We show that deformation acts their Mellin transform, mul...

A bstract We build a connection between topology of smooth 4-manifolds and the theory topological modular forms by considering topologically twisted compactification 6d (1 , 0) theories on with flavor symmetry backgrounds. The effective 2d has (0 1) supersymmetry and, possibly, residual symmetry. equivariant Witten genus this then produces new invariant 4-manifold equipped principle bundle, val...

Abstract Let X be a complex smooth quasi-projective surface acted upon by finite group G such that the quotient $X/G$ has singularities only of ADE type. We obtain an explicit expression for generating series Euler characteristics zero-dimensional components in moduli space subschemes invariant under action G. show this (up to suitable rational power formal variable) is holomorphic modular form.