All Questions

Let $K$ be a totally real number field of class number 1, and $Q$ the quaternion algebra over the ring of integers of $K$ with basis $\{1,i,j,k\}$ such that $i^2 = j^2 = k^2 = -1$ and $ij = -ji, ik = ...

$\DeclareMathOperator\Mat{Mat}$How to construct an explicit isomorphism of the split quaternion algebra $(a,b)_F$ over the field $F$ to $\Mat_2(F)$? As it is known that the algebra of quaternions is ...

$\DeclareMathOperator\ch{ch}$$\DeclareMathOperator\FPdim{FPdim}$We refer to [EGNO15, Chapter 3] for the notion of fusion ring and basic results. The type of a fusion ring $R$ is the list $(\FPdim(b_i)...

Given a number $n$ and an Interval $I = [ \; \lfloor n^{1/4} \rfloor, \lfloor n^{(1/3) \rfloor \;} ]$, can we say anything about the distribution of $\{ n \mod b \;\;| \; b \in I \}$? In particular, ...

For $0\leq k\leq n$ integers let $P_k(n):= n^k,\ S_k(n):= P_k(1)+\ldots P_k(n)= 1^k+\ldots n^k$. Then $P_k(0)=0$, $S_0(n)=n$. For calculate $S_1(n)$ i consider: $$P_2(n)-P_2(n-1)=2n+1$$ then $\begin{...