Extended Riemann hypothesis

Statement

The conjecture is as follows.

For any prime $p$, the smallest quadratic nonresidue modulo $p$ is less than $3(\log p{)}^2/2$. Here, $\log$ denotes the natural logarithm.

Related facts and conjectures

Weaker conjectures

• Riemann hypothesis

Weaker facts

• Smallest quadratic nonresidue is less than squareroot plus one