M. Emory

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math.NT2026

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.NT2024

Beyond Endoscopy via Poisson Summation for GL(2,K)

Melissa Emory, Malors Espinosa-Lara, Debanjana Kundu +1

In the early 2000's, R. Langlands proposed a strategy called Beyond Endoscopy to attack the principle of functoriality, which is one of the central questions of present day mathema…