406 articles
Spectral Theory & the Hilbert–Pólya Program
Recasting the zeros of ζ(s) as eigenvalues of a self-adjoint operator.
The ideas that resurface again and again across our research insights — and why each one keeps leading back to the Riemann Hypothesis.
16 themes across 829 articles
Each segment is one theme, sized by how many articles explore it — together they map where the search for a proof keeps returning.
An article can touch several themes, so each percentage is a share of all theme tags rather than of the 829 published articles.
Recasting the zeros of ζ(s) as eigenvalues of a self-adjoint operator.
How evenly the primes are spread, and what RH would pin down.
Zeros as fixed points of flows and features of geometric spaces.
Randomness, entropy, and statistical physics applied to the zeros.
Verification, complexity theory, and machine methods on the zeros.
The wider family of zeta-like functions and their shared symmetry.
The classical toolkit: contour integrals, analytic continuation, the functional equation.
Zeta zeros statistically resemble eigenvalues of large random matrices.
Determinants, field extensions, and algebraic invariants of the zeros.
Harmonic analysis, the Mellin transform, and convolution identities.
RH is equivalent to a sequence of numbers all being non-negative.
The dictionary linking primes to zeros, and the strip we can clear.
RH as an inequality about the sum of divisors of every integer.
Borrowing structure from genetics, morphogenesis, and living systems.
RH controls how much the Möbius function can accumulate.
Studying all primes at once through adèles and local fields.