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+----- Thread: A proof of Riemann Hypothesis ? (/showthread.php?tid=1867)
A proof of Riemann Hypothesis ? - mklabgr - 09-05-2026
Quote:This not an accepted proof of the Riemann Hypothesis. As of September 2026, the Clay Mathematics Institute still officially lists the Riemann Hypothesis as unsolved, which decisively tells us that de Branges's 2017 manuscript has not achieved general mathematical acceptance.
The reason for mentioning his proof of RH is to expose the level of sophistication involved.
Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He was the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana, retiring in 2023. He is best known for proving the long-standing Bieberbach conjecture in 1984,
summary
Louis de Branges’s 89-page 2017 manuscript claims a proof of the Riemann Hypothesis by placing the Riemann zeta function inside a much broader framework involving Hilbert spaces of entire functions, weighted Hardy/Stieltjes spaces, harmonic and Fourier analysis, quaternionic or “skew-plane” structures, adelic constructions, and Hecke operators. He constructs generalized zeta functions whose Dirichlet-series coefficients arise as eigenfunctions of Hecke operators and argues that their zero distributions can be controlled through the maximal accretive property of a Radon transformation: in the nonsingular case this property is supposed to imply the corresponding Riemann hypothesis directly, while in the singular case a parity decomposition is used to remove the obstruction. The classical Euler–Riemann zeta function $\zeta(s)$ is then claimed as a special case, which would imply that every nontrivial zero satisfies $\operatorname{Re}(s)=\tfrac12$.
ARTICLE [PDF]