Related papers: An explicit inversion formula for the $p$-adic Whi…

For a reductive group $G$ over a non-Archimedean local field (e.g $GL_n( \mathbb{Q}_p )$ ), Jacquet's Whittaker function is essentially proportional to a character of an irreducible representation of the Langlands dual group $G^\vee(…

Bertolini-Darmon and Mok proved a formula of the second derivative of the two-variable $p$-adic $L$-function of a modular elliptic curve over a totally real field along the Hida family in terms of the image of a global point by some…

The subject of the present paper is an application of quantum probability to $p$-adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for ${\rm PGL}_2(F)$, where $F$ is a $p$-adic field. As a…

We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth representations of GL(n,F) where F is a finite extension of Q_p and l is different from p. To do so, we also extend the theory of Rankin-Selberg integrals, first…

We develop a Fourier--analytic framework for establishing spectral reciprocity formulas linking $\mathrm{GL}_3$ and $\mathrm{GL}_2$ automorphic spectra over number fields. The method applies uniformly to cuspidal and non-cuspidal…

We formulate p-adic versions of following three: (1) Grothendieck Inequality, (2) Johnson-Lindenstrauss Flattening Lemma, (3) Bourgain-Tzafriri Restricted Invertibility Theorem.

The $b$-Whittaker functions are eigenfunctions of the modular $q$-deformed $\mathfrak{gl}_n$ open Toda system introduced by Kharchev, Lebedev, and Semenov-Tian-Shansky. Using the quantum inverse scattering method, the named authors obtained…

Recent advances have extended the Dunkl transform to the setting of Clifford algebras. In particular, the two-sided quaternionic Dunkl transform has been introduced as a Dunkl analogue of the two-dimensional quaternionic Fourier transform.…

In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…

We consider a class of equations with the fractional differentiation operator $D^\alpha$, $\alpha >0$, for complex-valued functions $x\mapsto f(|x|_K)$ on a non-Archimedean local field $K$ depending only on the absolute value $|\cdot |_K$.…

We obtain an explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations. We have another integral expression different from that of Miyazaki [7].

In this paper we give a proof of the Lefschetz fixed point formula of Freed$^{\rm [1]}$ for an orientation-reversing involution on an odd dimensional spin manifold by using the direct geometric method introduced in [2] and then we…

We investigate how fields transform under the Poincar\'e group in nonrelativistic effective field theories of QCD. In constructing these transformations, we rely only on symmetries and field redefinitions to limit the number of allowed…

In this work we study the relationship between several combinatorial formulas for type $A$ spherical Whittaker functions. These are spherical functions on $p$-adic groups, which arise in the theory of automorphic forms. They depend on a…

We completely characterize the boundedness of the Volterra type integration operators $J_b$ acting from the weighted Bergman spaces $A^p_\alpha$ to the Hardy spaces $H^q$ of the unit ball of $\mathbb{C}^n$ for all $0<p,q<\infty$. A partial…

Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are used to construct new examples of…

We identify q-deformed gl(l+1)-Whittaker functions with a specialization of Macdonald polynomials. This provides a representation of q-deformed gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie algebra \hat{gl(l+1)}.…

We establish the existence of smooth transfer for Guo-Jacquet relative trace formulae in $p$-adic case. This kind of smooth transfer is a key step towards a generalization of Waldspurger's result on central values of L-functions of $GL_2$.

Let H be a split reductive group over a local non-archimedean field, and let H^ denote its Langlands dual group. We present an explicit formula for the generating function of an unramified L-function associated to a highest weight…

In 2014, Darmon and Rotger defined the Garrett-Rankin triple product $p$-adic $L$- function and related it to the image of certain diagonal cycles under the $p$-adic Abel- Jacobi map. We introduce a new $p$-adic triple symbol based on this…