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

Stephan Ramon Garcia, George Todd

Published 2018-04-19Version 1

We connect the sixth moment of Kloosterman sums to elliptic curves and provide an elementary proof that Kloosterman sums $K_u$ with $p\nmid u$ are $O(p^{2/3})$. In particular, we can break the $O(p^{3/4})$ barrier without deep tools.