MathOverflow

I am currently at the stage of selecting a topic for my Master’s thesis, and I am torn between two directions that, while both rooted in number theory, offer very different technical flavors:
Dirichlet's Theorem on Arithmetic Progressions and Probabilistic Primality Testing...

The convergence of the series $S = \sum_{n=1}^\infty \frac{|\sin n|^n}{n}$ was settled by T. Tao (#282259), but the quantitative relationship between this sum and its continuous integral remains unexplored to my knowledge. I have investigated the discretization...

Let $A=KQ/I$ be a finite dimensional quiver algebra with connected acyclic quiver $Q$ and admissible relations $I$.Let $W$ be the Cartan matrix of $A$ (which we can assume to be lower triangular with ones on the diagonal).Let $M:=W-id$, which is a nilpotent...

let a contracted sequence $x_1,x_2,\dots$ of values be characterized by $x_i\ne x_{i+1}$, i.e. a sequence after adjacent duplicates have been replaced by a single value.
Then, given an infinite sequence $\Sigma:=x_1,x_2,\dots$ of real values, I define its min-max tree as follows:...