14 citations · 18 across the 5 of their papers we have counts for
5 papers
Linear independence in linear systems on elliptic curves
Bradley W. Brock, Bruce W. Jordan, Bjorn Poonen +2
Let be an elliptic curve, with identity , and let be a cyclic subgroup of odd order , over an algebraically closed field with . For…
Polynomials with a common composite
Robert M. Beals, Joseph L. Wetherell, Michael E. Zieve
Let f and g be nonconstant polynomials over an arbitrary field K. In this paper we study the intersection of the polynomial rings K[f] and K[g], and in particular we ask whether th…
Curves of every genus with many points, II: Asymptotically good families
Noam D. Elkies, Everett W. Howe, Andrew Kresch +3
We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a…
On the genera of X_0(N)
János A. Csirik, Joseph L. Wetherell, Michael E. Zieve
Let g_0(N) be the genus of the modular curve X_0(N). We record several properties of the sequence {g_0(N)}. Even though the average size of g_0(N) is 1.25N/pi^2, a random positive…
Curves of every genus with many points, I: Abelian and toric families
Andrew Kresch, Joseph L. Wetherell, Michael E. Zieve
Let N_q(g) denote the maximal number of F_q-rational points on any curve of genus g over the finite field F_q. Ihara (for square q) and Serre (for general q) proved that limsup_{g-…