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- W2964004180 abstract "Consider the Weil sum $W_{F,d}(u)=sum_{x in F} psi(x^d+u x)$, where $F$ is a finite field of characteristic $p$, $psi$ is the canonical additive character of $F$, $d$ is coprime to $|F^*|$, and $u in F^*$. We say that $W_{F,d}(u)$ is three-valued when it assumes precisely three distinct values as $u$ runs through $F^*$: this is the minimum number of distinct values in the nondegenerate case, and three-valued $W_{F,d}$ are rare and desirable. When $W_{F,d}$ is three-valued, we give a lower bound on the $p$-adic valuation of the values. This enables us to prove the characteristic $3$ case of a 1976 conjecture of Helleseth: when $p=3$ and $[F:{mathbb F}_3]$ is a power of $2$, we show that $W_{F,d}$ cannot be three-valued." @default.
- W2964004180 created "2019-07-30" @default.
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- W2964004180 date "2015-04-01" @default.
- W2964004180 modified "2023-10-16" @default.
- W2964004180 title "Divisibility of Weil sums of binomials" @default.
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- W2964004180 doi "https://doi.org/10.1090/proc/12687" @default.
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