2 papers
math.GM2026
Spectral Geometry of the Primes
Douglas F. Watson
We construct a family of self-adjoint operators on the prime numbers whose entries depend on pairwise arithmetic divergences, replacing geometric distance with number-theoretic dis…
math.SP2026
Spectral-Dimension Obstructions for Operators with Superlinear Counting Laws
Douglas F. Watson, Tiziano Valentinuzzi
We show that single-valuation exponential kernels, under mild regularity assumptions, converge in the continuum limit to a fourth-order operator with heat asymptotics $Î(t)\sim t^…