3 papers
math.NT2025
Sums of Exponential Terms, Conserved Quantities, and the Real Wave Numbers
Terence R. Smith
There is consensus that sums of complex exponential terms, despite their mathematical significance, only possess closed-form representations f…
math.NT2025
Rational Wave Numbers and the Algebraic Structure of the Cyclic Groups of the Roots of Unity
Terence R. Smith
Rational wave numbers are periodic sequences in which amplitude a product of powers of trigonometric sequences and ${\bf w}(f,g)=\exp({\…
cs.DS2022
Natural Wave Numbers, Natural Wave Co-numbers, and the Computation of the Primes
Terence R. Smith
The paper exploits an isomorphism between the natural numbers N and a space U of periodic sequences of the roots of unity in constructing a recursive procedure for representing and…