MathOverflow

Let
[\eta(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^s},\qquad s=\sigma+it.]
I am studying a block decomposition of the Dirichlet eta function in which the summation indices are partitioned into exponentially growing intervals. Specifically, I define

We can define a shift-invariant space as$$V_{\varphi}(\mathbb{Z}):=\left\{\sum_{k\in\mathbb{Z}}c_k\varphi({\cdot}-k):(c_k)\in \ell_2\right\},$$where convergence of the series is taken to be in $L^2(\mathbb{R})$. Is this a closed subspace of $L^2(\mathbb...

Let $M_{2,4}(\mathbb{R})$ be the set of real $2\times4$-matrices of rank $2$. For any $A\in M_{2,4}(\mathbb{R})$ and $1\leq i<j\leq 4$, let $p_{ij}$ be the corresponding $2\times 2$-minors of $A$. The image $K_{2,4}$ of the Plücker map$$\mathcal...

Is this iterative approach to solving congruences a known technique?
Problem
I'm trying to solve systems of linear congruences without requiringpairwise coprime moduli.