Heidi Goodson

activity

20132024

most citedTowards the Sato-Tate Groups of Trinomial Hyperelliptic Curves

7 citations · 11 across the 9 of their papers we have counts for

collaborators

12 papers

math.NT2024

Nondegeneracy and Sato-Tate Distributions of Two Families of Jacobian Varieties

Melissa Emory, Heidi Goodson

We consider the curves $y^{2} = x^{2^{m}} - 1$ and $y^{2} = x^{2^{d} + 1} - x$ over the rationals. These curves are related via their associated Jacobian varieties in that the Jacobians of the la…

math.NT2023

Mod $ℓ$ gamma factors and a converse theorem for finite general linear groups

Jacksyn Bakeberg, Mathilde Gerbelli-Gauthier, Heidi Goodson +3

The local converse theorem for Rankin-Selberg gamma factors of $GL_{2} (F_{q})$ proved by Piatetski-Shapiro over $C$ no longer holds after reduction modulo $\…

math.NT2022★ 2 cited

An Exploration of Degeneracy in Abelian Varieties of Fermat Type

Heidi Goodson

The term degenerate is used to describe abelian varieties whose Hodge rings contain exceptional cycles -- Hodge cycles that are not generated by divisor classes. We can see the eff…

math.NT2021

Sato-Tate Distributions of Catalan Curves

Heidi Goodson

For distinct odd primes $p$ and $q$ , we define the Catalan curve $C_{p, q}$ by the affine equation $y^{q} = x^{p} - 1$ . In this article we construct the Sato-Tate groups of the Jacobians in…

math.HO2021

Examining the Modeling Framework of Crime Hotspot Models in Predictive Policing

Heidi Goodson, Alanna Hoyer-Leitzel

Predictive policing has its roots in crime hotspot modeling. In this paper we give an example of what goes into mathematical crime hot spot modeling and show that the modeling assu…

math.NT2020★ 2 cited

Sato-Tate Distributions of $y^{2} = x^{p} - 1$ and $y^{2} = x^{2 p} - 1$

Melissa Emory, Heidi Goodson

We determine the Sato-Tate groups and prove the generalized Sato-Tate conjecture for the Jacobians of curves of the form $y^{2} = x^{p} - 1 and y^{2} = x^{2 p} - 1,$ where $p$ is an o…

math.CO2019

An Identity for Vertically Aligned Entries in Pascal's Triangle

Heidi Goodson

The classic way to write down Pascal's triangle leads to entries in alternating rows being vertically aligned. In this paper, we prove a linear dependence on vertically aligned ent…

math.NT2018★ 7 cited

Towards the Sato-Tate Groups of Trinomial Hyperelliptic Curves

Melissa Emory, Heidi Goodson, Alexandre Peyrot

We consider the identity component of the Sato-Tate group of the Jacobian of curves of the form $C_{1} : y^{2} = x^{2 g + 2} + c, C_{2} : y^{2} = x^{2 g + 1} + c x, C_{3} : y^{2} = x^{2 g + 1} + c,$ …

math.NT2017

Hypergeometric Properties of Genus 3 Generalized Legendre Curves

Heidi Goodson

Inspired by a result of Manin, we study the relationship between certain period integrals and the trace of Frobenius of genus 3 generalized Legendre curves. We show that both of th…

math.NT2016

A Complete Hypergeometric Point Count Formula for Dwork Hypersurfaces

Heidi Goodson

We extend our previous work on hypergeometric point count formulas by proving that we can express the number of points on families of Dwork hypersurfaces $$X_λ^d: \hspace{.1in} x_1…

math.NT2015

Hypergeometric Functions and Relations to Dwork Hypersurfaces

Heidi Goodson

We give an expression for number of points for the family of Dwork K3 surfaces $X_{λ}^{4} : x_{1}^{4} + x_{2}^{4} + x_{3}^{4} + x_{4}^{4} = 4 λ x_{1} x_{2} x_{3} x_{4}$ over finite fields of order $q\equiv…

math.NT2013

Effective Congruences for Mock Theta Functions

Nickolas Andersen, Holley Friedlander, Jeremy Fuller +1

Let M(q)=\sum c(n) q^n be one of Ramanujan's mock theta functions. We establish the existence of infinitely many linear congruences of the form c(An+B) \equiv 0 (mod \ell^j), where…

Nondegeneracy and Sato-Tate Distributions of Two Families of Jacobian Varieties

Mod ℓ gamma factors and a converse theorem for finite general linear groups

An Exploration of Degeneracy in Abelian Varieties of Fermat Type

Sato-Tate Distributions of Catalan Curves

Examining the Modeling Framework of Crime Hotspot Models in Predictive Policing

Sato-Tate Distributions of y2=xp−1 and y2=x2p−1

An Identity for Vertically Aligned Entries in Pascal's Triangle

Towards the Sato-Tate Groups of Trinomial Hyperelliptic Curves

Hypergeometric Properties of Genus 3 Generalized Legendre Curves

A Complete Hypergeometric Point Count Formula for Dwork Hypersurfaces

Hypergeometric Functions and Relations to Dwork Hypersurfaces

Effective Congruences for Mock Theta Functions

Mod $ℓ$ gamma factors and a converse theorem for finite general linear groups

Sato-Tate Distributions of $y^{2} = x^{p} - 1$ and $y^{2} = x^{2 p} - 1$