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arXiv · 2112.07700

Improving and Maximal Inequalities for Primes in Progressions

Christina Giannitsi·Michael T. Lacey·Hamed Mousavi·Yaghoub Rahimi
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Abstract

Assume that $ y < N$ are integers, and that $ (b,y) =1$. Define an average along the primes in a progression of diameter $ y$, given by integer $ (b,y)=1 $. \begin{align*} A_{N,y,b} := \frac{\phi (y)}{N} \sum _{\substack{n N _{y,r}} \lvert A_{N,y,b} f \rvert \rVert_{r}\ll \lVert f\rVert_{r}. \end{align*} The implied constant is only a function of $ r$. The uniformity over progressions imposes several novel elements on the proof.

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Christina Giannitsi, Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi. 2021-12-14. Improving and Maximal Inequalities for Primes in Progressions. https://arxiv.org/abs/2112.07700

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