MathOverflow

Let $B=(B_t)_{0\le t\le T}$ be a continuous semi-martingale and $\mathbb F=(\mathcal F_t)_{0\le t\le T}$ be its natural filtration. Denote by $\mathcal C_b(\Omega\times \mathbb R_+)$ the space of continuous bounded functions $F:\Omega\times \mathbb R...

A classic example of a non-affine scheme is to glue two copies of a DVR along the generic point. The resulting scheme has just $3$ points, is not affine, and if also not separated. This begs the question. Does there exists a scheme with finitely many...

Given a trivariate in $\mathbb Z[x,y,z]$ of shape
$$f(x,y,z) = x^2+a xy+b xz+cx+dy+ez+f\in\mathbb Z[x,y,z]$$ having $$\|f(Xx,Yy,Zz)\|_\infty=W$$ for some integers $(X,Y,Z)\in\mathbb Z_+^3$ and the condition is there is an unique $$(x',y',z')\in\mathbb Z^3\cap(-X,X)\times(-Y,Y)\times(-Z,Z):f(x',y',z...

Let
$$H_i^{(2)}=\sum_{k=1}^{i}\frac{1}{k^2}.$$
It is well known that, for every prime $p > 7$,