Related papers: Computing Hilbert modular forms as orthogonal modu…
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…
We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.
We utilize effective algorithms for computing in the cohomology of a Shimura curve together with the Jacquet-Langlands correspondence to compute systems of Hecke eigenvalues associated to Hilbert modular forms over a totally real field.
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
In this paper we describe various applications of the Riemann-Hilbert method to the theory of orthogonal polynomials on the line and on the circle.
We describe a method to compute Hurwitz-Hodge integrals.
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
In this article we present an algorithm that uses the graded algebra structure of Hilbert modular forms to compute the adelic $q$-expansion of Hilbert modular forms of weight one as the quotient of Hilbert modular forms of higher weight.…
We recall first the analytic theory of the Hilbert modular varieties of level $\Gamma_1(\mathfrak{c},\mathfrak{n})$ and their compactifications. We construct arithmetic toroidal compactifications of the universal Hilbert-Blumenthal abelian…
We describe the computation of tables of Hilbert modular forms of parallel weight 2 over totally real fields.
We present several new heuristic algorithms to compute class polynomials and modular polynomials modulo a prime $p$ by revisiting the idea of working with supersingular elliptic curves. The best known algorithms to this date are based on…
We compute the Hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules.
In this note, we present a systematic method to explicitly compute the determinants and inverses for some generalized Hilbert matrices associated with orthogonal systems with explicit representations. We expressed the determinant, the…
We study the degree of the special cubic fourfolds in the Hilbert scheme of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signature (2, 20).
We give a simple iterative procedure to compute the classical conformal blocks on the sphere to all order in the modulus.
The aim of this paper is to introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module $M$ over the polynomial ring $K[X_1,..., X_n]$ by reducing the problem to…
We present two approaches that can be used to compute modular forms on noncongruence subgroups. The first approach uses Hejhal's method for which we improve the arbitrary precision solving techniques so that the algorithm becomes about up…
We generalize the work of Ohta on the congruence modules attached to elliptic Eisenstein series to the setting of Hilbert modular forms. Our work involves three parts. In the first part, we construct Eisenstein series adelically and compute…
The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…
Unlike classical modular forms, there is currently no general way to implement the computation of Siegel modular forms of arbitrary weight, level and character, even in degree two. There is however, a way to do it in a unified way. After…