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 F. The design of algorithms for the enumeration of automorphic forms has emerged as a major theme in computational… (More)
In the first part of this thesis, building on ideas of R. Pollack and G. Stevens, we present an efficient algorithm for integrating certain rigid analytic functions attached to automorphic forms on definite quaternion algebras. We then apply these methods, in conjunction with the Jacquet-Langlands correspondence and the uniformization theorem of… (More)
We define a cocycle on GL n (Q) using Shintani's method. This construction is closely related to earlier work of Solomon and Hill, but differs in that the cocycle property is achieved through the introduction of an auxiliary perturbation vector Q. As a corollary of our result we obtain a new proof of a theorem of Diaz y Diaz and Friedman on signed… (More)
We use Kneser's neighbor method and isometry testing for lattices due to Plesken and Souveigner to compute systems of Hecke eigenvalues associated to definite forms of classical reductive algebraic groups.
In this course and project description, we briefly present the following: • The statement of Stark's rank one abelian conjecture and of the central motivating problem of this lecture series, namely: can we give (conjectural) exact formulas for Stark's units? • The claim that this question has an affirmative answer via the construction of explicit cycles in… (More)