Abstract
We establish a large sieve bound for expressions of the form $$\sum\limits_{r=1}^R \left\vert \sum\limits_{M < n\le M+N} a_ne\left(\alpha_rf(n)\right)\right\vert^2,$$ where $f(x)=\alpha x^2+\beta x+\theta\in \mathbb{R}[x]$ is a quadratic polynomial with $\alpha>0$ and $\beta\ge 0$. We also consider the case when $f(x)=x^d$ with $d\in \mathbb{N}$, $d\ge 3$.
Citation
Stephan Baier. "The large sieve with quadratic amplitude." Funct. Approx. Comment. Math. 36 33 - 43, January 2006. https://doi.org/10.7169/facm/1229616440
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