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math.NT2025
Hypergeometric decomposition of Delsarte K3 pencils
Rachel Davis, Jessamyn Dukes, Thais Gomes Ribeiro +4
We study five pencils of projective quartic Delsarte K3 surfaces. Over finite fields, we give explicit formulas for the point counts of each family, written in terms of hypergeomet…
math.NT2018
Cohomology groups of Fermat curves via ray class fields of cyclotomic fields
Rachel Davis, Rachel Pries
The absolute Galois group of the cyclotomic field acts on the étale homology of the Fermat curve of exponent . We study a Galois cohomology group which…
math.NT2018
Arithmetic of quaternion origami
Rachel Davis, Edray Herber Goins
We study origami with -Galois cover . For a point , we study the field obtained by adjoini…
math.NT2018
A note on the procedure to find the generic polynomial of a quotient (closely following Adelmann)
Rachel Davis
There are 3 examples in these notes. The first one is the standard example of the cubic resolvent of a quartic. The second example is exactly from Adelmann \cite{Adelmann} and give…