相关论文: A remark on the failure of multiplicity one for GS…

We obtain a sharp refinement of the strong multiplicity one theorem for the case of unitary non-dihedral cuspidal automorphic representations for GL(2). Given two unitary cuspidal automorphic representations for GL(2) that are not…

Using recent results, we prove strong multiplicity one theorems for Goss zeta functions and their Teichmuller lifts.

It is known that multiplicity one property holds for SL(2), while the strong multiplicity one property fails. However, in this paper, we show that if we require further that a pair of cuspidal representations $\pi$ and $\pi'$ of SL(2) have…

We prove several multiplicity one theorems in this paper. For k a local field not of characteristic two, and V a symplectic space over k, any irreducible admissible representation of the symplectic similitude group GSp(V) decomposes with…

We show that a weak form of the generalized Bocherer's conjecture implies multiplicity one for Siegel cusp forms of degree 2.

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let $\pi$ be a unitary, cuspidal, automorphic representation of $GL_n(\A_K)$. Let $S$ be a set of finite places of $K$, such that the sum $\sum_{v\in…

We prove the classification of discrete automorphic representations of GSp$_4$ explained in [Art04], as well as a compatibility between the local Langlands correspondences for GSp$_4$ and Sp$_4$ .

One of the important technical tools in Gaitsgory's proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([3]) is the theory of Whittaker functors for GL_n. We define Whittaker functors for GSp_4 and study…

We prove an analogue of the strong multiplicity one theorem in the context of $\tau_n$-spherical representations of the group $G = SO(2,1)^\circ$ appearing in $L^2(\Gamma_i \backslash G)$ for uniform torsion-free lattices $\Gamma_i, i = 1,…

We give a simple quaternionic proof of a recent result of Goldmakher and Pollack on restricted sums of four integral squares.

We consider multivariate polynomials and investigate how many zeros of multiplicity at least $r$ they can have over a Cartesian product of finite subsets of a field. Here r is any prescribed positive integer and the definition of…

I this paper, which is a sequel to math.AG/0310361, we study Bessel models of representations of GSp_4 over a local non archimedian field in the framework of the geometric Langlands program. The Bessel module over the nonramified Hecke…

Using Zeilberger's algorithm, we here give a proof of the supercongruence $$ \sum_{n=0}^{\frac{p^r-3}{4}}(8n+1)\frac{\left(\frac{1}{4}\right)_n^4}{(1)_n^4}\equiv -p^3…

In this paper, we extend the article that Minkowski problem in Gaussian probability space of Huang et al. to $L_p$-Gaussian Minkowski problem, and obtain the existence and uniqueness of $o$-symmetry weak solution in case of $p\geq1$.

Publications on automorphic representations of the group U(3) assumed the validity of multiplicity one theorem since I claimed it in 1982. But the argument, published 1988, was based on a misinterpretation of a claim of Gelbart and…

In general the multiplicity one theorem fails for Fourier-Jacobi models over finite fields. In this paper we prove that there is an upper bound for the multiplicities of Fourier-Jacobi models which is independent of $q$. As a consequence,…

For distinct unitary cuspidal automorphic representations $\pi_1$ and $\pi_2$ for $\mathrm{GL}(2)$ over a number field $F$ and any $\alpha\in\Bbb{R}$, let $\mathcal{S}_{\alpha}$ be the set of primes $v$ of $F$ for which…

We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula [1]p does not have maximal unifiers, and exhibit an…

Let $p$ be an odd prime. Define the Gaussian power sum \[ G_n(p)=\sum_{a=1}^{p-1}\sum_{b=1}^{p-1}(a+bi)^n\in\mathbb Z[i]. \] We determine $G_p(p)$ modulo high powers of $p$: if $p\equiv 1\pmod 4$ then $$G_p(p)\equiv p^2(1+i)\pmod{p^3},$$…

We prove spectral analogues of the classical strong multiplicity one theorem for newforms. Let $\Gamma_1$ and $\Gamma_2$ be uniform lattices in a semisimple group $G$. Suppose all but finitely many irreducible unitary representations (resp.…