Marco Mantovanelli

collaborators

10 papers

math.GM2026

A Divisor-Weighted Golomb Sequence: Zeta Asymptotics and Arithmetic Fluctuations

Marco Mantovanelli

We study a divisor-weighted version of Golomb's self-description: the nondecreasing sequence $A$ in which each positive integer $m$ occurs $\sum_{d ∣ m} A (d)$ times. This rule has…

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.GM2026

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers

Marco Mantovanelli

For an odd perfect number $N$ , write $q = min {p : p ∣ N}$ for its smallest prime divisor. This paper proves a certified branch-closure theorem for the five minimal-prime branches…

math.CO2026

Averaged Extensions of Golomb's Triangular Recursion: Critical Invariance and Supercritical Constraints

Marco Mantovanelli

For an integer $m \geq 1$ and a parameter $α > 0$ , consider the nested recursion $$ Q_{α,m}(n)=1+\left\lfloor \fracα{m}\sum_{j=1}^m Q_{α,m}\!\left(n-Q_{α,m}(n-j)\right)\right\rfloor, \…

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…

math.CO2026

Certified Return-Word Induction for a Perturbed Hofstadter Recursion

Marco Mantovanelli

We study the parity-perturbed Hofstadter recursion $Q (1) = Q (2) = 1, Q (n) = Q (n - Q (n - 1)) + Q (n - Q (n - 2)) + (- 1)^{n} .$ We prove that it is well-defined for every $n \geq 1$ by a computer-a…

math.CO2026

Quadratic Reduction and Classical Multiple-Index Fibonacci-Lucas Identities

Marco Mantovanelli

We place several classical identities in a common algebraic framework. Let $x$ be an element of a unital algebra over a commutative ring $R$ satisfying $x^{2} - t x + d 1 = 0.$ Then ever…

math.CO2026

A Dyadic Frequency Law for a Perturbed Hofstadter $Q$ -Recursion

Marco Mantovanelli

We study the perturbed Hofstadter $Q$ -recursion $Q (1) = Q (2) = 1, Q (n) = Q (n - Q (n - 1)) + Q (n - Q (n - 2)) + (- 1)^{n} (n \geq 3) .$ Cloître proved that the recursion is globally well-defi…

A Divisor-Weighted Golomb Sequence: Zeta Asymptotics and Arithmetic Fluctuations

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

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

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

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers

Averaged Extensions of Golomb's Triangular Recursion: Critical Invariance and Supercritical Constraints

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

Certified Return-Word Induction for a Perturbed Hofstadter Recursion

Quadratic Reduction and Classical Multiple-Index Fibonacci-Lucas Identities

A Dyadic Frequency Law for a Perturbed Hofstadter Q-Recursion

A Dyadic Frequency Law for a Perturbed Hofstadter $Q$ -Recursion