Semiprime-Order Circulant Determinants: A Conductor-65 Counterexample, Reciprocal Unit Bases, and a Prime-Norm Classification
Abstract
This preprint addresses three questions raised by Paudel and Pinner concerning integer circulant determinants of semiprime order. It proves that ±5³ and ±13³ do not occur at order 65, establishes a reciprocal and skew-reciprocal unit-basis theorem for odd cyclotomic fields, and classifies the corresponding prime-norm problem. The deposit includes the complete source, verification materials, and reproducible exact computations.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Differential Equations and Dynamical Systems
Analytic Number Theory Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 August 2026
- Language
- EN
- Document type
- Preprint