MathOverflow

I hope this is a suitable MO question. I am interested in knowing if there are any bounds on the error of the sum of the Mobius function $\mu$ over short arithmetic progressions. Let,
\begin{equation}f(A,B) = \sum\limits_{k=A}^{B}\mu(k)\end{equation}\begin{equation}f_e(A,B) = |f(A,B) - (B-A)|\end{equation}...

Let $E$ be a subset of $\mathbb R$ with Hausdorff dimension $0 < \dim_H (E) < 1$.
We write $E + E$, $E \cdot E$ for the sets of sums and products of elements of $E$ respectively.
Question: Is it possible that

Let $\mathbb{F}_q$ be a finite field. Consider the finite field $\mathbb{F}_{q^3}$ as a $3$-dimensional vector space over $\mathbb{F}_q$. Let V be the $8$-dimensional $\mathbb{F}_q$-vector space given by $V=\{(x,y,z,t)\mid x,t\in \mathbb{F}_q, y,z\in...

Introducing nonstandard analysis and the infinitesimals it allows, we consider the axiomatic extension of nonstandard analysis as a Nelsonian IST.
If the zero point of ζ(s) is infinitesimal at ε_0,
It is conceivable that re(s) = 1/2 + ε_0.