# Heights

## The Morm is Dead! Long Live the Morm!

Let $K$ be a number field of degree $d$ over $\mathbb Q$. Let $\mathfrak F$ be the group of fractional ideals of $K$, and let $\mathcal N$ and $\mathfrak N$ be respectively the elements of… Read More »The Morm is Dead! Long Live the Morm!

## Multiplicative Distance Functions

A positive definite function $\Phi: \mathbb C[x] \rightarrow [0, \infty)$ is a multiplicative distance function if for any monic $f, g \in \mathbb C[x],$ $\Phi(f g) = \Phi(f) \Phi(g)$ and there exists a homogeneity degree… Read More »Multiplicative Distance Functions

## Some Inner Product Calculations

In Nathan Hunter’s thesis, the inner product of two monomials $x^M$ and $x^L$, with $M \leq L$ are given as \begin{eqnarray}\langle x^M , x^L \rangle &=& 2 \pi \sum_{n=-NM}^M {M \choose \frac{NM + n}{N+1}} {L… Read More »Some Inner Product Calculations