Publications (30)
Hypergeometric -functions in average polynomial time, II
Edgar Costa, Kiran S. Kedlaya, David Roe
For a fixed positive integer , we describe an algorithm for computing, for all primes , the mod- reduction of the trace of Frobenius at of a fixed hypergeomet…
Rigorous computation of the endomorphism ring of a Jacobian
Edgar Costa, Nicolas Mascot, Jeroen Sijsling +1
We describe several improvements to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field.
Asymptotic expansions, -values and a new Quantum Modular Form
Edgar Costa, Korneel Debaene, João Guerreiro
In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function of Kontsevich. Here we produce a new example of a quantu…
Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
Raymond van Bommel, Shiva Chidambaram, Edgar Costa +1
We describe an efficient algorithm which, given a principally polarized (p.p.) abelian surface over with geometric endomorphism ring equal to , compute…
Curve equations from expansions of 1-forms at a nonrational point
Raymond van Bommel, Edgar Costa, Bjorn Poonen +1
We exhibit an algorithm to compute equations of an algebraic curve over a computable characteristic 0 field from the power series expansions of its regular 1-forms at a nonrational…
Counting points on smooth plane quartics
Edgar Costa, David Harvey, Andrew V. Sutherland
We present efficient algorithms for counting points on a smooth plane quartic curve modulo a prime . We address both the case where is defined over and the…