Marco Mantovanelli

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math.NT2026

The Right Edge of the Zero Set of the Fibonacci Zeta Function

Marco Mantovanelli

Let $F_{1} = F_{2} = 1$ , $F_{n + 2} = F_{n + 1} + F_{n}$ , and define the Fibonacci zeta function by $Z_{F} (s) = n \geq 1 \sum F_{n}^{- s}, Re s > 0.$ We determine the exact right edge o…

math.NT2026

A Two-Variable Zeta Function for a Parity-Perturbed Hofstadter Q-Recursion: The Exceptional t = -1 Slice and Gaussian Boundary Layers

Marco Mantovanelli

We study the parity-perturbed Hofstadter $Q$ -recursion $$ \widetilde Q(1)=\widetilde Q(2)=1,\qquad \widetilde Q(n)=\widetilde Q(n-\widetilde Q(n-1)) +\widetilde Q(n-\widetilde Q(n-…

math.NT2026

Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite Numbers

Marco Mantovanelli

Let $d (n)$ be the divisor function and let $H < H^{'}$ be consecutive highly composite numbers. We study directed unit moves between their prime-exponent vectors under the hard ceiling…

math.NT2026

The Subtractive Divisor Orbit: Unconditional Bounds, Parity Constraints, and a Conditional Framework

Marco Mantovanelli

Let $τ (n)$ denote the number of positive divisors of $n$ . Starting from $n_{0} = x$ , consider the orbit $n_{j + 1} = n_{j} - τ (n_{j})$ , and let $a (x)$ be its hitting time of zero. Although the a…