Christian T'afula

activity

20242026

collaborators

6 papers

math.NT2026

Thin subbases of Piatetski-Shapiro sequences

Christian TÃ¡fula

For a non-integral real number $c > 1$ , let $N_{(c)} := {⌊ n^{c} ⌋ ∣ n \in N}$ . We show that $N_{(c)}$ contains thin subbases of every order $h\ge…

math.NT2026

Waring and Waring-Goldbach subbases with prescribed representation function

Christian TÃ¡fula

Let $h \geq 2$ . For $A \subseteq N$ write \[ r_{A,h}(n) := \#\{(x_1,\ldots,x_h)\in A^h ~|~ x_1+\cdots+x_h=n\}. \] We prove a general probabilistic subbasis principle: assumi…

math.NT2026

Representation functions with prescribed rates of growth

Christian TÃ¡fula, Christian Táfula

Fix an integer $h \geq 2$ , and let $b_{1}, \dots, b_{h}$ be (not necessarily distinct) positive integers with $g cd (b_{1}, \dots, b_{h}) = 1$ . For any subset $A \subseteq N$ , le…

math.NT2025

Multiplicative recurrence of MÃ¶bius transformations

Sun-Kai Leung, Christian TÃ¡fula

We establish a complete characterization of multiplicative recurrence for images of the positive integers under MÃ¶bius transformations, answering a question of Donoso--Le--Moreira…

math.CO2024

Knights are 24/13 times faster than the king

Christian TÃ¡fula

On an infinite chess board, how much faster can the knight reach a square when compared to the king, in average? More generally, for coprime $b > a \in Z_{\geq 1}$ such that…

math.GR2024

Classification of the conjugacy classes of $SL (2, R)$

Christian TÃ¡fula

In this note, we classify the conjugacy classes of $SL_{2} (R)$ , the universal covering group of $PSL_{2} (R)$ . For any non-central elemen…

Thin subbases of Piatetski-Shapiro sequences

Waring and Waring-Goldbach subbases with prescribed representation function

Representation functions with prescribed rates of growth

Multiplicative recurrence of MÃ¶bius transformations

Knights are 24/13 times faster than the king

Classification of the conjugacy classes of SL(2,R)

Classification of the conjugacy classes of $SL (2, R)$