26 citations · 45 across the 10 of their papers we have counts for
13 papers
Generating sets for maximal orders in rational quaternion algebras
Kirsten Eisenträger, Eyal Z. Goren, Annamaria Iezzi +6
Given a maximal order in a rational definite quaternion algebra, and a prime coprime to the discriminant of , this paper considers subsets of $\…
First-order theory of a field and its Inverse Galois Problem
Francesca Balestrieri, Jennifer Park, Alexandra Shlapentokh
Let be a finite group. Then there exists a first-order statement in the language of rings without parameters and depending only on such that, for any field , we h…
Computing endomorphism rings of supersingular elliptic curves and connections to pathfinding in isogeny graphs
Kirsten Eisentraeger, Sean Hallgren, Chris Leonardi +2
Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of th…
Everywhere local solubility for hypersurfaces in products of projective spaces
Tom Fisher, Wei Ho, Jennifer Park
We prove that a positive proportion of hypersurfaces in products of projective spaces over are everywhere locally soluble, for almost all multidegrees and dimensions,…
Cycles in the supersingular -isogeny graph and corresponding endomorphisms
Efrat Bank, Catalina Camacho-Navarro, Kirsten Eisentraeger +2
We study the problem of generating the endomorphism ring of a supersingular elliptic curve by two cycles in -isogeny graphs. We prove a necessary and sufficient condition for…
Effective Chabauty for symmetric powers of curves
Jennifer Park
Faltings' theorem states that curves of genus have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound o…
A heuristic for boundedness of ranks of elliptic curves
Jennifer Park, Bjorn Poonen, John Voight +1
We present a heuristic that suggests that ranks of elliptic curves over the rationals are bounded. In fact, it suggests that there are only finitely many elliptic curves of rank gr…
As Easy as : Hilbert's Tenth Problem for Subrings of the Rationals and Number Fields
Kirsten Eisentraeger, Russell Miller, Jennifer Park +1
Hilbert's Tenth Problem over the field of rational numbers is one of the biggest open problems in the area of undecidability in number theory. In this paper we construc…
Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
Lisa Berger, Chris Hall, René Pannekoek +5
We study the Jacobian of the smooth projective curve of genus with affine model over the function field , when is p…
Insufficiency of the Brauer-Manin obstruction for Enriques surfaces
Francesca Balestrieri, Jennifer Berg, Michelle Manes +2
In 2011, Vàrilly-Alvarado and the last author constructed an Enriques surface over with an étale-Brauer obstruction to the Hasse principle and no algebraic Brauer-…
Faithful realizability of tropical curves
Man-Wai Cheung, Lorenzo Fantini, Jennifer Park +1
We study whether a given tropical curve in can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented…
Comparing arithmetic intersection formulas for denominators of Igusa class polynomials
Jacqueline Anderson, Jennifer S. Balakrishnan, Kristin Lauter +2
Bruinier and Yang conjectured a formula for intersection numbers on an arithmetic Hilbert modular surface, and as a consequence obtained a conjectural formula for CM(K).G_1 under s…
A universal first order formula defining the ring of integers in a number field
Jennifer Park
We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_…