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José
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Let $\mathbb{F}_q$ be a finite field, $\psi$ be a non-trivial additive character over $\mathbb{F}_q$, and $a, b \in \mathbb{F}_q$ constants. Is there any known estimate for the gaussian sum

$$\sum_{x \in \mathbb{F}_q} \psi( a x^m + b x^n),$$

possibly for specific values of $m, n \in \mathbb{Z}_{\ge 2}$, $m \ne n$?

Let $\mathbb{F}_q$ be a finite field, $\psi$ be a non-trivial additive character over $\mathbb{F}_q$, and $a, b \in \mathbb{F}_q$ constants. Is there any known estimate for the gaussian sum

$$\sum_{x \in \mathbb{F}_q} \psi( a x^m + b x^n),$$

possibly for specific values of $m, n \in \mathbb{Z}_{\ge 2}$?

Let $\mathbb{F}_q$ be a finite field, $\psi$ be a non-trivial additive character over $\mathbb{F}_q$, and $a, b \in \mathbb{F}_q$ constants. Is there any known estimate for the gaussian sum

$$\sum_{x \in \mathbb{F}_q} \psi( a x^m + b x^n),$$

possibly for specific values of $m, n \in \mathbb{Z}_{\ge 2}$, $m \ne n$?

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José
  • 219
  • 1
  • 5

Known estimate for gaussian sum $\sum_{x \in \mathbb{F}_q} \psi( a x^m + b x^n)$?

Let $\mathbb{F}_q$ be a finite field, $\psi$ be a non-trivial additive character over $\mathbb{F}_q$, and $a, b \in \mathbb{F}_q$ constants. Is there any known estimate for the gaussian sum

$$\sum_{x \in \mathbb{F}_q} \psi( a x^m + b x^n),$$

possibly for specific values of $m, n \in \mathbb{Z}_{\ge 2}$?