Related papers: A note on Maass forms of icosahedral type

In the present paper, we will show that three apparently disjoint objects: Galois representations arising from twenty-seven lines on a cubic surface (number theory and arithmetic algebraic geometry), Picard modular forms (automorphic…

We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli…

Duke, Imamoglu, and Toth constructed a polyharmonic Maass form of level 4 whose Fourier coefficients encode real quadratic class numbers. A more general construction of such forms was subsequently given by Bruinier, Funke, and Imamoglu.…

We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects, suggesting some underlying combinatorics. We…

We combine the Duke-Imamoglu-Ikeda lifting with the theta lifting to produce new CAP representations of metaplectic, symplectic and orthogonal groups. These constructions partially generalize the theories of Waldspurger on the Shimura…

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of…

We study the sum of additively twisted Fourier coefficients of a symmetric-square lift of a Maass form invariant under the full modular group. Our bounds are uniform in terms of the spectral parameter of the Maass form, as well as in terms…

In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating function, the associated continued fraction, the orthogonality…

The Fourier coefficients of a smooth $K$-invariant function on a compact symmetric space $M=U/K$ are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we…

Kohnen and Sengupta proved that two cusp forms of different integral weights with real algebraic Fourier coefficients have infinitely many Fourier coefficients of the same as well as of opposite sign, up to the action of a Galois…

We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GL(N) Maass cusp forms for all N larger than 2, satisfy a central limit theorem in a…

In this paper, a strong multiplicity one theorem for Katz modular forms is studied. We show that a cuspidal Katz eigenform which admits an irreducible Galois representation is in the level and weight old space of a uniquely associated Katz…

We study the signs of the Fourier coefficients of a newform. Let $f$ be a normalized newform of weight $k$ for $\Gamma_0(N)$. Let $a_f(n)$ be the $n$th Fourier coefficient of $f$. For any fixed positive integer $m$, we study the…

Given a pair of n-dimensional complex Galois representations over Q, we define their matching density to be the density, if it exists, of the set of places at which the traces of Frobenius of the two Galois representations are equal. We…

By assuming the existence of (quasi)-linear Regge trajectories for heavy mesons, we derive new quadratic mass relations of non-Gell-Mann-Okubo type, 6M^2(q-qbar)+3M^2(c-cbar)=8M^2(c-qbar), 20M^2(q-qbar)+5M^2(b-bbar)= 16M^2(b-qbar),…

A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval $(0,1)$ is studied. This type of polynomials have direct applications in…

The matrix elements of unitary $SU_q(3)$ corepresentations, which are analogues of the symmetric powers of the natural repesentation, are shown to be the bivariate $q$-Krawtchouk orthogonal polynomials, thus providing an algebraic…

The zeros of D'Arcais polynomials, also known as Nekrasov--Okounkov polynomials, dictate the vanishing of the Fourier coefficients of powers of the Dedekind functions. These polynomials satisfy difference equations of hereditary type with…

Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…