59 citations · 371 across the 37 of their papers we have counts for
4 papers · 1 filter
Counting polynomials over finite fields with given root multiplicities
Ayah Almousa, Melanie Matchett Wood
We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Be…
The distribution of points on superelliptic curves over finite fields
GilYoung Cheong, Melanie Matchett Wood, Azeem Zaman
We give the distribution of points on smooth superelliptic curves over a fixed finite field, as their degree goes to infinity. We also give the distribution of points on smooth m-f…
Semiample Bertini theorems over finite fields
Daniel Erman, Melanie Matchett Wood
We prove a semiample generalization of Poonen's Bertini Theorem over a finite field that implies the existence of smooth sections for wide new classes of divisors. The probability…
Discriminants in the Grothendieck Ring
Ravi Vakil, Melanie Matchett Wood
We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singular…