4 citations · 5 across the 2 of their papers we have counts for
8 papers · 1 filter
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…
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…