Preprints and notes. My peer-reviewed papers are linked on ORCID.
This paper proves the prime number theorem by comparing how often each integer remains after deleting either K or K + 1 largest prime factors from every squarefree integer up to a common bound.
The paper describes the singular spectrum of a sparse matrix with determinant equal to the Mertens sum, counts exactly how many singular values equal one, and replaces earlier bounds for the smallest with an unconditional asymptotic formula.
How similarly do sites in a network operate? An interactive example using Earth Mover’s Distance to compare their production distributions.
Resolves a 2020 conjecture on the Perron vector of the totient Gram matrix and sharpens that paper’s eigenvalue and Möbius-correlation bounds to asymptotics.
The recent news from mathematics matters because it is a leading indicator of how knowledge work will evolve.
An affine-plane hypergraph with a polynomial-size description requires ℓ1 diversity distortion of order √n, refuting Conjecture 1.7 of Jozefiak and Shepherd.
Weighting the Liouville sum by a power of the square part of n moves its real pole without moving the zeros of ζ, so the sign of the sum reads a zero-free half-plane, and a real-character twist puts 1/L(σ,χ) into the residue.
Matching several histograms on a line at the cost of each unit’s bin span: weighted range costs turn out to be the only symmetric Monge costs with hull invariance and Minkowski additivity, and every vertex of the transport dual is counted.
A short note giving elementary proofs of several exact identities for weighted Möbius and Liouville sums, organized around a single convolution factorization, together with a two-way character-transfer bound.
A numerically certified face-by-face solver fills the low-ratio gap in Mangasarian’s Newton method on synthetic tests, matches production-solver timing on the largest cases, and narrows the gap on the Netlib benchmark through a three-method frontier, though it still trails HiGHS.
We construct an infinite tower of skew Hadamard matrices of orders 4(76t+3 + 1), t ≥ 0, beginning with order 1,376, using one fixed order-18 finite-field construction.
A systematic attack on Turyn’s 1972 converse conjecture closes every remaining non-prime-power case through q = 2000 and proves a semiprime nonexistence theorem, while the full conjecture remains open.
The paper extends earlier work on harmonic divisor matrices to a much sparser version of the Redheffer matrix, bounding its smallest singular value and determining its largest.
An iterated convex relaxation always converges to a fixed point, can stop finitely near regular CAZAC sequences, and has an exact regularity count at Zadoff–Chu points.
The paper settles two conjectures about harmonic divisor matrices and describes the extreme eigenvalues and singular values of a family linking them to the classical Redheffer matrix.
A direct formula for a real Hadamard matrix of order 2q(q + 1) for every prime power q ≡ 1 (mod 4), with proof and exact checks.
A recursive construction for partitioned difference families with geometric block sizes, with a proof and exact verification code.
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