Related papers: Slopes in eigenvarieties for definite unitary grou…

We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erd\H{o}s and R\'enyi and recent results of Kuryliak and Skaskiv. Our results are…

A homogeneous nilpotent Lie group has a scaling automorphism determined by a grading of its Lie algebra. Many proofs of upper bounds for the Dehn function of such a group depend on being able to fill curves with discs compatible with this…

Using the modularity technique of Wiles, we study the Hecke algebra of weight 2 and prime level N localized at the Eisenstein primes. On the way, we recover some results of Mazur ("Modular Curves and the Eisenstein Ideal") from a…

In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices $\mathrm{E}_7$, $\mathrm{E}_8$ and $\mathrm{E}_8\oplus \mathrm{A}_1$,…

We show that if an operator T is bounded on weighted Lebesgue space L^2(w) and obeys a linear bound with respect to the A_2 constant of the weight, then its commutator [b,T] with a function b in BMO will obey a quadratic bound with respect…

We obtain an asymptotic formula for a weighted sum over cuspidal eigenvalues in a specific region, for $\SL_2$ over a totally real number field $F$, with discrete subgroup of Hecke type $\Gamma_0(I)$ for a non-zero ideal $I$ in the ring of…

Let $\mathcal{H}$ be a noncommutative regular projective curve over a perfect field $k$. We study global and local properties of the Auslander-Reiten translation $\tau$ and give an explicit description of the complete local rings, with the…

We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\'ar for classical expansion of bounded…

Let $p$ be prime. We prove that, for $n$ odd, the $p$-torsion part of $\pi_q(S^{n})$ has cardinality at most $p^{2^{\frac{1}{p-1}(q-n+3-2p)}}$, and hence has rank at most $2^{\frac{1}{p-1}(q-n+3-2p)}$. For $p=2$ these results also hold for…

We describe a new method to bound certain higher-dimensional exponential sums which are associated with tori in symplectic groups over finite fields. Our method is based on the self-reducibility property of the Weil representation. As a…

We consider the higher order buckling eigenvalues of the following Dirichlet poly-Laplacian in the unit sphere $(-\Delta)^p u=\Lambda (-\Delta) u$ with order $p(\geq2)$. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the…

We study the geometry of the $p$-adic Siegel eigenvariety $\mathcal{E}$ of paramodular tame level at certain Saito-Kurokawa points having a critical slope. For $k \geq 2$ let $f$ be a cuspidal new eigenform of…

Let F be a square integrable Maass form on the Siegel upper half space of rank 2 for the Siegel modular group Sp(4, Z) with Laplace eigenvalue lambda. If, in addition, F is a joint eigenfunction of the Hecke algebra, we show a power-saving…

We obtain a full asymptotic expansion for orthogonal polynomials with respect to weighted area measure on a Jordan domain $\mathscr{D}$ with real-analytic boundary. The weight is fixed and assumed to be real-analytically smooth and strictly…

Let $T$ be a bounded linear operator on $L^p$. We study the rate of growth of the norms of the powers of $T$ under resolvent conditions or Ces\`aro boundedness assumptions. Actually the relevant properties of $L^p$ spaces in our study are…

We consider the Hodge Laplacian $\Delta$ on the Heisenberg group $H_n$, endowed with a left-invariant and U(n)-invariant Riemannian metric. For $0\le k\le 2n+1$, let $\Delta_k$ denote the Hodge Laplacian restricted to $k$-forms. Our first…

For prime $p\equiv-1\bmod d$ and $q$ a power of $p$, we obtain the slopes of the $q$-adic Newton polygons of $L$-functions of $x^d+ax^{d-1}\in \mathbb{F}_q[x]$ with respect to finite characters $\chi$ when $p$ is larger than an explicit…

We prove rate of convergence results for singular perturbations of Hamilton-Jacobi equations in unbounded spaces where the fast operator is linear, uniformly elliptic and has an Ornstein-Uhlenbeck-type drift. The slow operator is a fully…

Jun-Muk Hwang and Ngaiming Mok have proved the rigidity of irreducible Hermitian symmetric spaces of compact type under Kaehler degeneration. I adapt their argument to the algebraic setting in positive characteristic, where cominuscule…

We study the action of the Hecke operators $U_n$ on the space $\mathcal R$ of rational functions in one variable, over $\mathbb C$. The main goal is to give a complete classification of the eigenfunctions of $U_n$. We accomplish this by…