Shubhrajit Bhattacharya

math.NT — Number Theory

Unconditional implications of the Quasi-Riemann Hypothesis

Contributed by Shubhrajit Bhattacharya

This record identifies published conclusions formerly obtained under RH or GRH whose proofs require only a fixed zero-free half-plane for Dirichlet $L$-functions, with further applications of finite-order Hecke $L$-functions over $\mathbb Q(\sqrt{-3})$. The input is the $7/8$ theorem stated in the recent OpenAI manuscript claiming to prove the quasi-Riemann Hypothesis. We give the uniform analytic deductions explicitly and distinguish them from previously established algebraic and combinatorial results used in the proofs. An accompanying audit records the source verification and rejected candidates. No theorem about all number-field or automorphic $L$-functions is inferred from the Dirichlet statement; the pure cubic and cubic-nonresidue applications separately identify the precise fixed-field Hecke input.