B. Cloitre

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20182026

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math.NT2026

Regular Arithmetic Functions, Volume I. Theory, Applications, Examples

Benoit Cloitre

This is the first of two volumes on regular arithmetic functions, and an introduction to their theory. A regular arithmetic function (RAF) is a kernel whose properties come from a…

math.NT2026

Fibonacci, Dirichlet, and Gauss in a single sum

Benoit Cloitre

We study the fractional-part sums $\sum_{k = 1}^{n} {F_{n} / F_{k}}$ , where $F_{n}$ is the $n$ th Fibonacci number. Their asymptotic behavior depends on the parity of $n$ . For odd $n$ , the r…

math.NT2026

The Thue-Morse Transform

Benoit Cloitre

We define the Thue-Morse transform T on a class of infinite binary words. It sends the alternating word a_0 = 010101... to the Thue-Morse sequence. We then study its orbit a_m = T^…

math.NT2026

Beatty solutions of almost Golomb functional equations

Benoit Cloitre

We study the almost Golomb equation of order $r$ , $a (S (n)) = n$ , where $S (n) = a (n) + a (n - 1) + \dots + a (n - r + 1)$ , for nondecreasing sequences of positive integers. Its greedy solu…

math.NT2026

The Mantovanelli-Hofstadter Sequence

Benoit Cloitre

We study the perturbed Hofstadter recurrence introduced by Mantovanelli, $Q (n) = Q (n - Q (n - 1)) + Q (n - Q (n - 2)) + (- 1)^{n}$ , with $\w…

math.NT2026

Meta-automatic Sequences

John M. Campbell, Benoit Cloitre

Nested (or meta-Fibonacci) recurrences, such as the recurrence used to define Hofstadter's Q-sequence, along with the digit-based recurrences that underlie automatic sequences are…