论文标题
v树 - 持续的分数扩展，船尾修饰树，minkowski的$？（x）$二进制功能：指数级更快
V Tree -- Continued Fraction Expansion, Stern-Brocot Tree, Minkowski's $?(x)$ Function In Binary: Exponentially Faster
论文作者
论文摘要
STERN-NOROCOT TREE和MINKOWKI的问号功能$？（X）$（或Conway的盒子功能）与Q的持续分数扩展，并通过对部分分母的单位编码进行了编码。我们首先定义了自然数的二进制编码$ c_i，c_i {ii} $，适用于gauß-kuz'min的措施，用于分配部分分母。然后，我们使用二进制包裹$ C_I，C_ {II} $将V $ _1 $ Tree定义为与Stern-Brocot树相似的类似物。我们将看到，所有具有分母$ q $的数字都存在于第一个$ 3.44 \ log_2（q）$ latver中，而不是$ 1/q $在船尾领域的级别$ q $中出现。 v $ _1 $树的扩展，V树，完全涵盖了Q的所有数字。我们还定义了Minkowski的问号功能的二进制版本，$？_ V $，并猜想它在理性点（对于原始点，$？'（x）= 0，x \ in q $）。
The Stern-Brocot tree and Minkowki's question mark function $?(x)$ (or Conway's box function) are related to the continued fraction expansion of numbers from Q with unary encoding of the partial denominators. We first define binary encodings $C_I, C_{II}$ of the natural numbers, adapted to the Gauß-Kuz'min measure for the distribution of partial denominators. We then define the V$_1$ tree as analogue to the Stern-Brocot tree, using the binary encondings $C_I, C_{II}$. We shall see that all numbers with denominator $q$ are present in the first $3.44\log_2(q)$ levels, instead of $1/q$ appearing in level $q$ in the Stern-Brocot tree. The extension of the V$_1$ tree, the V tree, covers all numbers from Q exactly once. We also define the binary version of Minkowski's question mark function, $?_V$, and conjecture that it has no derivative at rational points (for the original, $?'(x)=0, x\in Q$).
