Related papers: Simultaneous computation of Hecke operators

We find a relation guaranteeing that Hankel operators realized in the space of sequences $\ell^2 ({\Bbb Z}_{+}) $ and in the space of functions $L^2 ({\Bbb R}_{+}) $ are unitarily equivalent. This allows us to obtain exhaustive spectral…

Dedekind symbols generalize the classical Dedekind sums (symbols). The symbols are determined uniquely by their reciprocity laws up to an additive constant. There is a natural isomorphism between the space of Dedekind symbols with…

We characterize the space of new forms for $\Gamma_0(m)$ as a common eigenspace of certain Hecke operators which depend on primes $p$ dividing the level $m$. To do that we find generators and relations for a $p$-adic Hecke algebra of…

We consider cuspidal representations in spaces of automorphic forms for the congruence subgroup $\Gamma_0(I)$ of Hilbert modular groups for some number field $F$. To each such representation are associated the eigenvalue $\lambda_j$ of the…

For a fixed prime p, we consider the (finite) set of supersingular elliptic curves over $\bar{\mathbb{F}}$. Hecke operators act on this set. We compute the asymptotic frequence with which a given supersingular elliptic curve visits another…

We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.

Let E_lambda be a Hilbert space, whose elements are functions spanned by the eigenfunctions of the Laplace-Beltrami operator associated with an eigenvalue lambda>0. The norm of elements in this space is given by the Petersson inner product.…

In this paper, we study the Drinfeld cusp forms for $\Gamma_1(T)$ and $\Gamma(T)$ using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the…

A description is given of all primitive differential series mod p of order 1 which are eigenvectors of all the Hecke operators and which are differential Fourier expansions of differential modular forms of arbitrary order and given weight;…

We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…

Let G be a torsion-free finite-index subgroup of SL(n,Z) or GL(n,Z), and let d be the cohomological dimension of G. We present an algorithm to compute the eigenvalues of the Hecke operators on the integral cohomology of degree d-1 for n =…

We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applications to the analytic theory of elliptic curves over a finite…

We determine the average size of the eigenvalues of the Hecke operators acting on the cuspidal modular forms space $S_k(\Gamma_0(N))$ in both the vertical and the horizontal perspective. The "average size" is measured via the quadratic…

Let X=G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial…

We compute the intertwining relation between the Hecke operators and the Siegel lowering operators on Siegel modular forms of arbitrary level $N$ and character $\chi$ by using formulas for the action of the Hecke operators on Fourier…

In this article, we compute the Hecke operator $\mathrm{T}_2$, associated to the Kneser $2$-neighbours, defined on the isomorphic classes of even lattices of determinant 2, in dimension 23 and 25. In a previous article, we computed some…

A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a…

Fix a prime N, and consider the action of the Hecke operator T_N on the space M_k(SL(2,Z)) of modular forms of full level and varying weight k. The coefficients of the matrix of T_N with respect to the basis {E_4^i E_6^j | 4i + 6j = k} for…

We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.

In the present article we define the algebra of differential modular forms and we prove that it is generated by Eisenstein series of weight $2,4$ and 6. We define Hecke operators on them, find some analytic relations between these…