The quasi-Riemann hypothesis: a fixed zero-free half-plane for zeta and all Dirichlet L-functions

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The quasi-Riemann hypothesis: a fixed zero-free half-plane for zeta and all Dirichlet L-functions parent of this event

Theorem 1 claims that every finite-order Hecke $L$-function over $\mathbb Q(\sqrt{-3})$ and every Dirichlet $L$-function, including $\zeta(s)$, has no zero in $\Re s>7/8$, the principal pole at $s=1$ excepted. So the nontrivial zeros of $\zeta$ have real part at most $7/8$, and any exceptional real zero in $(7/8,1)$ is excluded. The proof runs through cubic theta series and sextic large sieves, first reaching $11/12$ and then refining to $7/8$; the Dirichlet case is transferred from the Hecke family. It does not prove the Riemann hypothesis or GRH, and says so; the boundary line $\Re s=7/8$ is not covered. A separate manuscript gives a different proof of the weaker half-plane $\Re s>11/12$. parent of this event

VibeMathed record: The quasi-Riemann hypothesis: a fixed zero-free half-plane for zeta and all Dirichlet L-functions evidence for this event

Vinogradov's least quadratic nonresidue conjecture evidence for this event

Companion: alternate proof of the zero-free half-plane Re s > 11/12 evidence for this event

Companion: Uniform exclusion of Landau-Siegel zeros evidence for this event

Lean: Dirichlet and zeta 7/8 nonvanishing (main declarations) evidence for this event

Lean comparator statement: zeta 7/8 bound evidence for this event

Lean comparator statement: Dirichlet 7/8 bound evidence for this event

Lean comparator statement: Hecke 7/8 bound over Q(sqrt(-3)) evidence for this event

Lean: release scope note (states the half-plane, not this corollary) evidence for this event

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