Related papers: A note on Poisson summation for GL(2)

Let $K$ be a field with $G_K(2) \simeq G_{\mathbb{Q}}(2)$, where $G_F(2)$ denotes the maximal pro-2 quotient of the absolute Galois group of a field $F$. We prove that then $K$ admits a (non-trivial) valuation $v$ which is 2-henselian and…

In this paper, we consider representations of $p$-adic classical groups parabolically induced from the products of shifted Speh representations and unitary representations of Arthur type of good parity. We describe how to compute the socles…

We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy…

We express the contribution of certain maximal parabolic Eisenstein series to the spectral side of the Arthur--Selberg trace formula for GL$(n)$ in terms of zeroes of Rankin--Selberg $L$-functions, generalizing previous results for GL(2)…

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along…

S. Orlik and M. Strauch have studied locally analytic principal series representation for general $p$-adic reductive groups generalizing an earlier work of P. Schneider for $GL(2)$ and related the condition of irreducibility of such locally…

We apply analytic perturbation theory to the Gross--Llewellyn Smith sum rule. We study the $Q^2$ evolution and the renormalization scheme dependence of the analytic three-loop QCD correction to this sum rule, and demonstrate that the…

In this article we study the Poisson summation for Hankel transform in the sense of Braverman-Kazhdan-Ngo in the special case of $L$-embedding $\rho: GL_1\rightarrow GL_2$. We view such a summation formula as the generalization of the…

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When…

The Landau-Selberg-Delange (LSD) method gives an asymptotic formula for the partial sums of a multiplicative function $f$ whose prime values are $\alpha$ on average. In the literature, the average is usually taken to be $\alpha$ with a very…

In our previous publications we have introduced analogs of partial derivatives on the algebras U(gl(N)). In the present paper we compare two methods of introducing these analogs: via the so-called quantum doubles and by means of a…

We develop generalized Petersson/Bruggeman-Kuznetsov (PBK) formulas for specified local components at non-archimedean places. In fact, we introduce two hypotheses on non-archimedean test function pairs $f \leftrightarrow \pi(f)$, called…

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure…

This article describes a purely analytic approach to urn models of the generalized or extended P\'olya-Eggenberger type, in the case of two types of balls and constant ``balance,'' that is, constant row sum. The treatment starts from a…

In this paper we continue the study of locally analytic representations of a $p$-adic Lie group $G$ in vector spaces over a spherically complete non-archimedean field $K$, building on the algebraic approach to such representations…

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra $\ssll (2)_q$ introduced by Lyubashenko and the second named author. We consider separately the cases of $q$ generic…

Analytic continuation of the perturbative series from spacelike to timelike regions is performed using renormalization group summed perturbation theory (RGSPT). This method provides an all-order summation of kinematic ``$\pi^2$-terms''…

The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a…

A commutative Poisson subalgebra of the Poisson algebra of polynomials on the Lie algebra of n x n matrices over ${\Bbb C}$ is introduced which is the Poisson analogue of the Gelfand-Zeitlin subalgebra of the universal enveloping algebra.…

For two distinguished prime $\ell$ and $p$, we prove a $\ell$-adic version of the Poisson formula for reductive $p$-adic groups. In order to do this we write an identity for the trace of regular representation and orbital integrals. Next we…