The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane Re(s) > 7/8
- Mathematics
There are absolute constants A,C>0 such that, for every odd prime p, the least positive quadratic nonresidue n(p) is at most C(log p)^A; hence n(p)≪δ p^δ for each δ>0.
OpenAI reports a polylogarithmic least nonresidue bound
- Mathematics
For every odd prime p, the least positive quadratic nonresidue is at most C(log p)^A for absolute constants A and C.
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Understand the problem ↓Understanding the problem
Read the background
For every odd prime p, the least positive quadratic nonresidue is at most C(log p)^A for absolute constants A and C.
Why it matters
If the manuscript’s zero-free theorem is correct, this corollary resolves Vinogradov’s least quadratic nonresidue conjecture.
What counts as progress
Is the least quadratic nonresidue modulo every odd prime p bounded by p^δ for each fixed δ>0?
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