# List of Lee’s Conjectures

Conj. 1: (Solved)
For any non-negative real number $r > 0$, there exists a set, $K$ of which strict Hausdorff Dimension is equal to $r$.

Fields: Measure Theory, Real Analysis
Proposed: 02.24.15
Solved: 03.16.15
The general outline is presented in the post, CONSTRUCTING A SET WITH ARBITRARY STRICT HAUSDORFF DIMENSION

Conj. 2: (Unsolved)
Let $p$ be a prime. Let $r_p$ denote the smallest primitive root of $(\mathbb{Z}/p\mathbb{Z})^\times$. Then, $\displaystyle \liminf_{p \to \infty} r_p$ is bounded, while $\displaystyle \limsup_{p \to \infty} r_p$ diverges.

Fields: Elementary Number Theory
Proposed: 10.28.14

Conj. 3: (Solved)
Let $\mathbb{P}$ be a set of primes. The supremum of $s$ such that $\displaystyle \sum_{p \in \mathbb{P}} \frac{1}{p^x}$ diverges is $x = 1$.

Fields: Analytic Number Theory
Proposed: 02.26.16
Solved: 03.17.16
The general outline is presented in the post, The Half-Plane of Convergence of Zeta Function, and it begot a new conjecture, Conj. 4.

Conj. 4: (Unsolved)
Let us define Prime Zeta Function as $\displaystyle P(s) = \sum_{p \in \mathbb{P}} \frac{1}{p^s}$ where $\mathbb{P}$ is a set of primes. The domain of $P(s)$ is all complex plane except $s = 1$ like Riemann Zeta Function.

Fields: Analytic Number Theory
Proposed: 03.17.16

The post is still in progress.