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Let's consider the family of sequences of coefficients in the expansion $$\prod_{i=0}^{n-1}(1+x^{3^i}+x^{3^{i+1}})=\sum_{k\geq0}a_n(k)\, x^k.$$ Remark. Evidently, the RHS is a finite sum. Here is a ...

What is $$p_*:=\inf\big\{p\in\mathbb R\colon\,\inf_{n\in\mathbb N}n^p\,\inf_{k\in\mathbb N} |2\sqrt{3n}-9\pi/4-k\pi|>0\big\},$$ where $\mathbb N:=\{1,2,\dots\}$? In other words, I would like to ...

I'm attempting to bound an expression of the form. $$ \lVert(\prod_{i=1}^{\infty} \phi_i) * s \rVert_{\infty} $$ Where $\phi_i$ are bounded periodic step functions which can be replaced by smoothed ...

A question was recently asked about a generalization of the Fejer-Jackson inequality $$\sum_{k=1}^n \frac{\sin kx}{k}\gt 0 \quad \forall\: n\in\mathbb{Z}^+\: \text{and}\: 0\lt x\lt\pi$$ to ...