Related papers: Revisiting Gamma conjecture I: counterexamples and…

We study complex projective manifolds X that admit surjective endomorphisms f:X->X of degree at least two. In case f is etale, we prove structure theorems that describe X. In particular, a rather detailed description is given if X is a…

We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension $n$ of the manifold and the dimension $\delta$ of its limit set. More precisely, we show that as $R\to\infty$, the…

Motivated by reformulating Furstenberg's $\times p,\times q$ conjecture via representations of a crossed product $C^*$-algebra, we show that in a discrete $C^*$-dynamical system $(A,\Gamma)$, the space of (ergodic) $\Gamma$-invariant states…

We consider the asymptotic behavior of the incomplete gamma functions gamma(-a,-z) and Gamma(-a,-z) as a goes to infinity. Uniform expansions are needed to describe the transition area z~a in which case error functions are used as main…

Let $\mathrm{IG}(k, 2n+1)$ be the odd-symplectic Grassmannian. Property $\mathcal{O}$, introduced by Galkin, Golyshev and Iritani for arbitrary complex, Fano manifolds $X$, is a statement about the eigenvalues of the linear operator…

We consider eigenvalues of the Dirichlet-to-Neumann operator for Laplacian in the domain (or manifold) with edges and establish the asymptotics of the eigenvalue counting function \begin{equation*} \mathsf{N}(\lambda)= \kappa_0\lambda^d…

In this paper we formulate a conjecture on the relationship between the equivariant \epsilon-constants (associated to a local p-adic representation V and a finite extension of local fields L/K) and local Galois cohomology groups of a Galois…

We investigate in the simplest compact D=4 N=1 Type IIB orientifold models the sigma-model symmetry suggested by the proposed duality of these models to heterotic orbifold vacua. This symmetry is known to be present at the classical level,…

We study Fano manifolds $X$ admitting an unsplit dominating family of rational curves and we prove that the Generalized Mukai Conjecture holds if $X$ has pseudoindex $i_X = (\dim X)/3$ or dimension $\dim X=6$. We also show that this…

Let $k$ be a real abelian number field and $p$ an odd prime not dividing $[k:\mathbb{Q}]$. For a natural number $d$, let $E_d$ denote the group of units of $k$ congruent to $1$ modulo $d$, $C_d$ the subgroup of $d$-circular units of $E_d$,…

The aim of the present paper is to give evidence, largely numerical, in support of the non-commutative main conjecture of Iwasawa theory for the motive of a primitive modular form of weight k>2 over the Galois extension of Q obtained by…

In their recent work, Garoufalidis and Kashaev extended the 3D-index of an ideally triangulated 3-manifold with toroidal boundary to a well-defined topological invariant which takes the form of a meromorphic function of 2 complex variables…

We study the fix point components of the big torus action on the moduli space of stable maps into a smooth projective toric variety, and apply Graber and Pandharipande's localization formula for the virtual fundamental class to obtain an…

For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to…

We consider a two-dimensional Lorentz-invariant field model with a $\phi^{4}$ potential modified by a term that introduces asymmetries at the manifold space. In this framework, the model recovers its original symmetry only when $p=0$. The…

Let $\tau$ denote the divisor function, and $f$ be any multiplicative function that satisfies some mild hypotheses. We establish the asymptotic formula or non-trivial upper bound for the shifted convolution sum $\sum_{n \leq…

We carry out the asymptotic analysis as $n \to \infty$ of a class of orthogonal polynomials $p_{n}(z)$ of degree $n$, defined with respect to the planar measure \begin{equation*} d\mu(z) = (1-|z|^{2})^{\alpha-1}|z-x|^{\gamma}\mathbf{1}_{|z|…

We consider $(p+1)$-form gauge fields in flat $(2p+4)$-dimensions for which the radiation and the Coulomb solutions have the same asymptotic falloff behavior. Imposing appropriate falloff behavior on fields and adopting a Maxwell-type…

We construct a gauged linear sigma-model representation and develop a 1/N-expansion for flag manifold sigma-models previously proposed by the author. Classically there exists a zero-curvature representation for the equations of motion of…

Given a number field $k$ and a quadratic extension $K_2$, we give an explicit asymptotic formula for the number of isomorphism classes of cubic extensions of $k$ whose Galois closure contains $K_2$ as quadratic subextension, ordered by the…