58 citations · 99 across the 16 of their papers we have counts for
19 papers
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…
A database of basic numerical invariants of Hilbert modular surfaces
Eran Assaf, Angelica Babei, Ben Breen +8
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
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…
Abelian varieties of prescribed order over finite fields
Raymond van Bommel, Edgar Costa, Wanlin Li +2
Given a prime power and , we prove that every integer in a large subinterval of the Hasse--Weil interval is $#A(\mathbb{F}_q)$…
Hypergeometric L-functions in average polynomial time
Edgar Costa, Kiran S. Kedlaya, David Roe
We describe an algorithm for computing, for all primes , the mod- reduction of the trace of Frobenius at of a fixed hypergeometric motive in time quasilinear in $X…
Effective obstruction to lifting Tate classes from positive characteristic
Edgar Costa, Emre Can Sertöz
We give an algorithm that takes a smooth hypersurface over a number field and computes a -adic approximation of the obstruction map on the Tate classes of a finite reduction. Th…
Restrictions on Weil polynomials of Jacobians of hyperelliptic curves
Edgar Costa, Ravi Donepudi, Ravi Fernando +3
Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hypere…
Arithmetic invariants from Sato--Tate moments
Edgar Costa, Francesc Fité, Andrew V. Sutherland
We give some arithmetic-geometric interpretations of the moments M_2[a_1], M_1[a_2], and M_1[s_2] of the Sato-Tate group of an abelian variety A defined over a number field by rela…
Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
Edgar Costa, Davide Lombardo, John Voight
Assuming the Mumford-Tate conjecture, we show that the center of the endomorphism ring of an abelian variety defined over a number field can be recovered from an appropriate inters…
Computing Zeta Functions of Cyclic Covers in Large Characteristic
Vishal Arul, Alex J. Best, Edgar Costa +2
We describe an algorithm to compute the zeta function of a cyclic cover of the projective line over a finite field of characteristic that runs in time . We conf…
Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in -adic cohomology
Edgar Costa, David Harvey, Kiran S. Kedlaya
We give an interim report on some improvements and generalizations of the Abbott-Kedlaya-Roe method to compute the zeta function of a nondegenerate ample hypersurface in a projecti…
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.
On the arithmetic of a family of degree-two K3 surfaces
Florian Bouyer, Edgar Costa, Dino Festi +2
Let denote the weighted projective space with weights over the rationals, with coordinates and ; let be the generic element of th…
On the distribution of the Picard ranks of the reductions of a surface
Edgar Costa, Andreas-Stephan Elsenhans, Jörg Jahnel
We report on our results concerning the distribution of the geometric Picard ranks of surfaces under reduction modulo various primes. In the situation that $\rk \Pic S_{\overl…
Traces, high powers and one level density for families of curves over finite fields
Alina Bucur, Edgar Costa, Chantal David +2
The zeta function of a curve over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix . We develop and present a new technique to…
Variation of Neron-Severi ranks of reductions of K3 surfaces
Edgar Costa, Yuri Tschinkel
We study the behavior of geometric Picard ranks of K3 surfaces over the rationals under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces mo…
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…
A search for Wilson primes
Edgar Costa, Robert Gerbicz, David Harvey
A Wilson prime is a prime p such that (p-1)! = -1 mod p^2. We report on a search for Wilson primes up to 2 * 10^13, and describe several new algorithms that were used in the search…
Faster deterministic integer factorization
Edgar Costa, David Harvey
The best known unconditional deterministic complexity bound for computing the prime factorization of an integer N is O(M_int(N^(1/4) log N)), where M_int(k) denotes the cost of mul…