Related papers: Fourier coefficients attached to small automorphic…

We discuss the approximation of real numbers by Fourier coefficients of newforms, following recent work of Alkan, Ford and Zaharescu. The main tools used here, besides the (now proved) Sato-Tate Conjecture, come from metric number theory.

We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions. This basis is natural from the point of view of principal…

Lapid and Mao formulated a conjecture on an explicit formula of Whittaker Fourier coefficients of automorphic forms on quasi-split classical groups and metaplectic groups as an analogue of Ichino-Ikeda conjecture. They also showed that this…

The Fourier Jacobi expansions of paramodular forms are characterized from among all formal series of Jacobi forms by two conditions on the Fourier coeffcients of the Jacobi forms: a growth condition and a set of linear relations. Examples,…

Let $\G\subset \mathrm{SL}_{2}(\R)$ be a cofinite Fuchsian subgroup, and let $i\infty$ be a cusp of $\G$. For $k\in\Z_{\geq 0}$, let $\Sk$ denote the complex vector space of cusp forms of weight-$k$, with respect to the Fuchsian subgroup…

We establish identities for the composition $T_{k,n}(|\widehat{gd\sigma}|^2)$, where $g\mapsto \widehat{gd\sigma}$ is the Fourier extension operator associated with a general smooth $k$-dimensional submanifold of $\mathbb{R}^n$, and…

Given a finite index subgroup of $SL_2(\mathbb Z)$ with modular curve defined over $\mathbb Q$, under the assumption that the space of weight $k$ ($ \ge 2$) cusp forms is $1$-dimensional, we show that a form in this space with Fourier…

Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4)))…

In this paper, we obtain under the assumption of the Generalized Riemann Hypothesis upper bounds for all high integral moments of sums of Fourier coefficients of a given modular form twisted by quadratic Dirichlet characters. We show the…

The Fourier coefficients of the Siegel-Eisenstein series are p-adically continued for all primes p, as meromorphic functions, using the reciprocal of a product of L-functions. A construction of p-adic meromorphic families of such series is…

We show that the Dirichlet series associated to the Fourier coefficients of a half-integral weight Hecke eigenform at squarefree integers extends analytically to a holomorphic function in the half-plane $\re s\textgreater{}\tfrac{1}{2}$.…

We study the following question: given a locally compact group when does its Fourier algebra coincide with the subalgebra of the Fourier-Stieltjes algebra consisting of functions vanishing at infinity? We provide sufficient conditions for…

We obtain resonances for short exponential sums involving Fourier coefficients of Maass forms for $\mathrm{SL}(n,\mathbb Z)$. This involves deriving asymptotics for the integrals appearing in the $\mathrm{GL}(n)$ Voronoi summation formula.…

We discuss Euclidean covariant vector random fields as the solution of stochastic partial differential equations of the form $DA=\eta$, where $D$ is a covariant (w.r.t. a representation \tau of $SO(d)$) differential operator with "positive…

Let $E$ be a non-Archimedian local field of characteristic zero and residue characteristic $p$. Let ${\bf G}$ be a connected reductive group defined over $E$ and $\pi$ an irreducible admissible representation of $G={\bf G}(E)$. A result of…

The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and are defined in terms of certain energies which capture Fourier decay. In this paper we obtain a convenient discrete…

Let $K/F$ be a finite Galois extension of number fields. It is well known that the Tchebotarev density theorem implies that an irreducible, finitely ramified $p$-adic representation $\rho$ of the absolute Galois group of $K$ is determined…

This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants $D$ such that…

It is known that automorphisms of finite-dimensional bound quiver algebras decompose into inner automorphisms and automorphisms which permute the vertices. In this paper, we show that for string algebras, automorphisms permuting vertices…

We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de…