George Todd

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20182021

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math.NT2021

Moments of Gaussian Periods and Modified Fermat Curves

Stephan Ramon Garcia, Brian Lorenz, George Todd

We use supercharacter theory to study moments of Gaussian periods. For $p - 1 = d k$ and fixed $k$ , we compute the fourth absolute moments for all but finitely many primes $p$ . For $d$ …

math.NT2018

Supercharacters, elliptic curves, and the sixth moment of Kloosterman sums

Stephan Ramon Garcia, George Todd

We connect the sixth power moment of Kloosterman sums to elliptic curves. This yields an elementary proof that $K_{u}$ with $p ∤ u$ are $O (p^{2/3})$ .